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Collection  de 
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Technical  and  Bibliographic  Notes/Notes  techniques  et  bibiiographiques 


The  institute  has  attempted  to  obtain  the  best 
original  copy  available  for  filming.  Features  of  this 
copy  which  may  be  bibliographlcally  unique, 
which  may  alter  any  of  the  images  in  the 
reproduction,  or  which  may  significantly  change 
the  usual  method  of  filming,  are  checiced  below. 


D 


0 


D 
D 


D 


Coloured  covers/ 
Couverture  de  couieur 


I      I   Covers  damaged/ 


Couverture  endommagie 


Covers  restored  and/or  laminated/ 
Couverture  restaurAe  et/ou  pelliculAe 


Cover  title  missing/ 

Le  titre  de  couverture  manque 


□   Coloured  maps/ 
Cartes  g^ographiques  en  couieur 

□   Coloured  ink  (i.e.  other  than  blue  or  blacit)/ 
Encre  de  couieur  (i.e.  autre  que  bleue  ou  noire) 

I      I   Coloured  plates  and/or  illustrations/ 


D 


Planches  et/ou  illustrations  en  couieur 

Bound  with  other  material/ 
RellA  avec  d'autres  documents 

Tight  binding  may  cause  shadows  or  distortion 
along  interior  margin/ 

La  reliure  serr^e  peut  causer  de  I'ombre  ou  de  la 
distortion  le  long  de  la  marge  intirieure 

Blank  leaves  added  during  restoration  may 
appear  within  the  text.  Whenever  possible,  these 
have  been  omitted  from  filming/ 
II  se  peut  que  certaines  pages  blanches  ajoutAes 
lors  d'une  restauration  apparaissent  dans  le  texte, 
mais,  iorsque  cela  Atait  possible,  ces  pages  n'ont 
pas  AtA  filmAes. 

Additional  comments:/ 
Commentaires  supplAmentaires: 


L'Institut  a  microf  llmA  le  meilleur  exemplaire 
qu'il  lul  M  AtA  possible  de  se  procurer.  Les  details 
de  cet  exemplaire  qui  sont  peut-Atre  uniques  du 
point  de  vue  bibliographique,  qui  peuvent  modifier 
une  image  reproduite,  ou  qui  peuvent  exiger  une 
modification  dans  la  mAthode  normale  de  filmage 
sont  Indiqute  ci-dessous. 


□   Coloured  pages/ 
Pages  de  couieur 

□    Pages  damaged/ 
Pages  endommagtes 

□   Pages  restored  and/or  laminated/ 
Pages  restaurtes  et/ou  pe.'MculAes 

I — I   Pages  discoloured,  stained  or  foxed/ 


D 


Pages  dAcolortes,  tachetAes  ou  piqutes 

Pages  detached/ 
Pages  d6tach6es 

Showthroughy 
Transparence 

Quality  of  prir 

Quality  inigale  de  I'impressior 

Includes  supplementary  materii 
Comprend  du  materiel  suppKmentaire 

Only  edition  available/ 
Seuie  Edition  disponible 


r~~1  Pages  detached/ 

Jr~l  Showthrough/ 

I      I  Quality  of  print  varies/ 

I     I  Includes  supplementary  material/ 

r~~|  Only  edition  available/ 


Pages  wholly  or  partially  obscured  by  errata 
slips,  tissues,  9tc.,  have  been  refiimed  to 
ensure  the  best  possible  Image/ 
Les  pages  totalement  ou  partiellement 
obscurcies  par  un  feuillet  d'errata,  une  pelure, 
etc.,  ont  6t6  fllmtes  A  nouveau  de  fapon  A 
obtenir  la  meilleure  image  possible. 


This  item  is  filmed  at  the  reduction  ratio  checked  tMlow/ 

Ce  document  est  fiim6  au  taux  de  reduction  indiquA  ci-dessous. 

10X  14X  18X  22X 


26X 


X 


12X 


16X 


20X 


24X 


Itol 


'e 

6tails 
m  du 
raodifiar 
tr  una 
llmaga 


B8 


arrata 

I  to 

i 

I  palura, 

on  A 


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32X 


Tha  copy  fiimad  hara  has  baan  raproducad  thanks 
to  tha  ganarosity  of: 

_,.       Library  of  Congrass 

Photoduplication  Sarvica 

Tha  imagas  appaaring  hara  9f  tha  bast  quality 
possibia  considaring  tha  condition  and  iagibility 
of  tha  original  copy  and  in  kaaping  with  the 
filming  contract  spacification^. 


Original  copias  in  printad  papar  covars  ara  fiimad 
baginning  with  tha  front  covar  and  anding  on 
tha  last  paga  with  a  printad  or  illustratad  impras* 
sion,  or  tha  back  covar  whan  appropriata.  All 
othar  original  copias  ara  fiimad  baginning  on  tha 
first  paga  with  a  printad  or  illustratad  impras- 
sion,  and  anding  on  tha  last  paga  with  a  printad 
or  illustratad  imprassion. 


Tha  last  racordad  frama  on  aach  microficha 
shall  contain  tha  symbol  — »>  (moaning  "CON- 
TINUED"), or  tha  symbol  V  (moaning  "END"), 
whichavar  applias. 

Maps,  platas,  charts,  ate.  may  ba  fiimad  at 
diffarant  raduction  ratios.  Thosa  too  larga  to  ba 
antiraly  includad  in  ona  axposura  ara  fiimad 
baginning  in  tha  uppar  laft  hand  cornar.  laft  to 
right  and  top  to  bottom,  as  many  framaa  as 
raquirad.  Tha  following  diagrams  lllustrata  tha 
mathod: 


t 

( 

a 

3 

L'axamplaira  fllmA  f ut  raproduit  grica  A  la 
gAnArositA  da: 

Library  of  Congrass 
Ph^tpduplication  Sarvica 


•*»*<?•/_ 


-;i# 


Las  imagas  suivantas  ont  *t4  raproduitas  avac  la 
plus  grand  soin,  compta  tanu  da  la  condition  at 
da  la  nattat*  da  l'axamplaira  filmA,  at  an 
conformity  avac  las  conditions  du  contrat  da 
fiimaga. 

Laa  axamplalras  originaux  dont  la  couvartura  an 
papiar  ast  ImprimAa  sont  filmte  9n  commandant 
par  la  pramiar  plat  at  an  tarminant  soit  par  la 
darnlAra  paga  qui  comporta  una  amprainta 
d'imprassion  ou  d'illustration.  soit  par  la  sacond 
plat,  salon  la  cas.  Tous  las  autras  axamplalras 
originaux  sont  filmte  an  commanqant  par  la 
pramiAra  paga  qui  compoiita  una  amprainta 
d'imprassion  ou  d'illustra*ion  at  an  tarminant  par 
la  darnlAra  paga  qui  comporta  una  talia 
amprainta. 

Un  das  symbolas  suhrants  apparattra  sur  la 
darnlAra  Imaga  da  chaqua  microficha,  salon  la 
cas:  la  symbols  — »>  signifia  "A  8UIVRE",  la 
symbols  V  signifia  "FIN". 

Las  cartas,  planchaa,  tablaaux,  ate,  pauvant  Atra 
fllmte  A  das  taux  da  rAductlon  diff Arants. 
Lorsqua  la  documant  ast  trop  grand  pour  Atra 
raproduit  mn  un  saul  cllchA,  11  ast  filmA  A  partir 
da  I'angla  supArlaur  gaucha,  da  gaucha  A  drolta. 
at  da  haut  an  bas.  an  pranant  la  nombra 
d'imagas  nAcassalra.  Las  diagrammas  suivants 
lllustrant  la  mAthoda. 


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5 

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A.PPE3Sri>IX     I. 


■  «0l^' 


DESCRIPTION 


or  THR 


TRANSIT    CIRCLE 


or  THB 


UNITED  STATES' NAVAL  OBSERVATORY, 


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i 


WITH  AM 


/ 


INVESTIGATION  OF  ITS  CONSTANTS, 


PBnpARn>  BT  emtmB,  or 
Rear  Admiral  CHARLES  HENRY  DAVIS,  U.  8.  N. 

■  VPRItlHTBiriDXVT, 

BY    SIMON>^NKWOOMB. 

noriMOBiwiun^uiiet, «. «.  h. 


/'WASHINGTON: 
OOVEBNMENT   PRINTING   OFFICE. 
1867. 


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TABLE  OF  CONTENTS. 


^••«^»«hm  of  lfc«  iaitrauMBt  and  Ht  a^aaste 

OtMty  ncOod  of  iannal%irtl«g  Ot «nran  or  » 1V«Mtt  Canh  .... .. 

&m"%MiM  «r  tiM  eoiMlMti  of  tin  IVHub  <%«d«  ud  ita  t^fridiHy 
IWtiftrMhwpNrfUawran , 

PeifonauMorthtiaitranaat 

A^MbitiMltedM. ...,.     ' 


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INTBODDCTORY  NOTE. 


The  imtrament  denribed  in  the  following  pages  wm  proonred  for  the  ObMrvatory  by  the 
late  Oaptaio  CKUIm.  On  hie  aeoewon  to  the  Saperintendency,  the  want  of  a  snttable  Meridian 
Circle  was  atrongly  felt.  The  military  operations  of  the  government  temporarily  delayed  the 
supply  of  this  want  In  October,  1868,  however,  the  necessary  authority  was  grant#.d  by  the 
Hon.  Secretary  of  the  Navy,  and  the  instrament  was  ordered  from  Messrs.  Pistor  and  Martins, 
of  Berlin.  Correspondence  respecting  the  sine  and  pbu  of  the  instrument  occupied  the  remain' 
der  of  the  yew,  and  terminated  by  concluding  on  an  object  glass  of  at  least  eight  Paris  inches 
dear  aperture,  and  by  leaving  the  plan  of  the  instrument  and  its  mountings  altogether  in  the 
bands  of  the  artiste. 

The  pa^s  of  the  instrument  arrived  in  October,  1866.  The  work  of  mounting  was  com- 
menced on  the  16th  of  that  month,  and  on  the  28th  the  instrument  was  in  position.  The  next 
two  months  were  occupied  in  determining  the  errors  of  flexure  and  division,  and  in  making  the 
necessary  preparations  for  active  work.  Begnfor  astronomical  observations  were  commenced 
on  January  8,  1866. 


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APPENDIX  I. 


DESCRIPTION 

or  TBI 

TRANSIT   CIRCLE 

OrTBC 

UNITED  STATES  NAVAL  OBSERVATORY. 


1 


i 


PAST    I. 

DB80BIPTI0N  OP  THE  INSTRUMENT  AND  ITS  ADJUNCTS. 
OENBBAL  DESCBIPTION.    (PLATE  m.) 

(1)  The  instrnmeDt  is  moanted  in  the  west  wing  of  the  Observatory,  the  room  formerly 
occapied  by  the  Transit  Instrument  The  interior  dimensions  of  the  room  are  24.3  feet  from 
east  to  west,  and  18.4  feet  from  north  to  south.  On  the  north  and  south  sides  of  the  room  are 
built  two  recesses,  each  six  feet  in  length,  and  six  in  depth,  to  make  room  for  the  collimators. 
The  slits  in  the  wall  and  roof  for  observing  are  thii'ty  inches  in  breadth,  and  closed  by  four 
shutters  on  the  roof,  and  a  door  on  each  side. 

(2)  The  piers  are  solid  monoliths  of  marble.  The  forur  of  each  pier  is  that  of  a  frustrnm  of 
a  pyramid,  surmounted  by  a  prism.  The  base  at  the  floor  me.>'iures  44  inches  from  north  to  south, 
and  38  inches  from  east  to  west.  The  top  of  the  pyramidal  portion  is  80  inches  above  the  floor, 
and  measures  18.6  inches  from  north  to  south,  by  24.6  from  east  to  west.  The  dimensions  of  the 
■laliiBg  horizontal  sections  of  the  prism  are  the  same,  while  the  heighv  of  the  prisms  is  28  inches; 
the  whole  height  of  the  piers  9  feet  above  the  floor.  The  inside  faces  of  the  piers  form  a  ver* 
tical  continuous  plane  19  inches  in  breadth,  and  9  feet  in  height.  On  each  side  of  this  plane 
the  stone  is  cut  away  in  the  form  of  a  section  of  a  hollow  cylinder.  The  distance  of  the  inside 
faces  is  64  inches.  A  cylindrical  hole  6  inches  in  diameter  is  cut  from  east  to  west  through 
each  prism  for  the  illumination. 

Into  these  openings  the  inside  ends  of  hollow  brass  cylinders  are  flrmly  set  with  plaster  to 
the  depth  of  6  inches.  The  outside  end  of  each  cylinder  expands  into  a  disk  8|  inches  in  diam* 
eter  and  0.7  of  an  inch  from  the  face  of  the  pier.  The  arms  which  cai:ry  the  four  reading  micro* 
scopes  of  each  circle  are  attached  to  these  disks,  radiating  from  the  central  axis  at  an  angle  of  46° 
from  the  horizontal  and  vertical  directions.  Within  each  disk,  near  its  centre,  is  a  system  of 
prismatic  reflectors  for  illuminating  the  divisions  of  the  circle.  The  illuminating  lamps  are 
each  at  the  large  end  of  a  conical  tube,  the  small  end  of  which  extends  through  the  opening  of 
the  pier  and  fits  into  the  interior  of  the  cylinder  carrying  the  microscope  disks.  The  large  end, 
carrying  the  lamp,  extends  three  feet  from  the  outer  face  of  the  pier.  One  lamp  illuminates 
the  field  of  the  telescope,  the  other  the  wires. 

The  Ys  are  fastened  into  semi-^cyliwlrioai  pieces  of  brara  which  extend  inward  from  the 
head  of  the  disk  carrying  the  microscope  arms,  the  axis  of  the  cylinder  being  a  continuation 
of  that  of  the  openings  in  the  pier,  as  shown  in  Plate  lY. 


2  DUBORTPnON  OF  THK  TBAi.lIT  OIBOUB  OP  TBI 

(3)  The  telescope  is  of  12  feet  focal  length,  and  8.6  inches  dear  apertare.  The  eye-piece 
is  furnished  with  a  system  of  twenty*three  fixed  vertical  wires,  (eight  of  which  it  is  intended  to 
remove,)  and  two  borizonta'  ones,  distant  8".  There  is  also  a  horizontal  and  a  vertical  microm* 
eter  screw,  the  former  carrying  one  vertical,  and  the  latter  four  horisontal  wires — a  central 
pair,  distant  ^".f>,  and  two  single  ones,  2^'  each  side  of  this  pair. 

(4)  The  circles  are  each  42  inches  in  diameter,  and  divided  on  silvc  to  every  S'.  The 
cylinder  on  the  clamp-end  of  tne  axis  also  has  a  coarser  division  to  every  10'  for  setting.  The 
general  character  of  the  arrangement  of  circles,  clamp,  counterpoises,  Ac,  may  be  seen  by  ref* 
erence  to  Plate  IV. 

Notwithstanding  its  dimensions,  the  instrument  is  reversible,  and  the  operation  of  revers' 
ing  can  be  performed  by  a  single  person  with  great  facility.     The  entire  weight  of  the  mov*  • 
able  part  of  the  instrument  is  only  about  900  pounds. 

(5)  The  sides  of  the  central  tube  of  the  telescope  are  pierced  by  openings  2)  inches  in 
diameter,  through  which  the  collimators  may  be  set  on  each  other  when  the  instrument  is  ver- 
tical.     These  are  not  shown  in  Plate  III. 

(6)  The  instrument  is  completely  spanned  from  north  to  south  by  an  arched  flight  of  steps 
for  reflection  observations  of  stars.  They  are  so  flgured  that  when  the  telescope  is  at  any  point- 
ing between  120°  and  240^  of  zenith  distance,  the  eye-piece  will  be  in  a  convenient  position  to 
look  into.  Above  the  fifth  step  the  arch  is  bifurcated,  so  as  not  to  interfere  with  the  line  of 
sight.  The  highest  step  is  a  platform  three  feet  in  length,  suspended  from  the  roof  by  iron 
bars  and  braces.     Hand-rails,  net  shown  in  the  plate,  extend  from  the  bars  nearly  to  the  floor. 

(7)  In  the  spring  of  1867  another  mechanical  improvement,  for  convenience  and  certainty 
in  observing  the  nadir  point,  was  introduced.  On  each  side  of  the  platform,  over  the  axis  of 
the  instrument,  a  seat  is  erected.  The  observer  can  sit  astride  of  either  seat  and  look  into  the 
eye-piece  when  the  telescope  points  to  the  nadir.  On  the  inside  of  each  seat,  between  the 
observer  and  the  telescope,  a  board,  eight  to  nine  inches  wide,  rises  from  the  platform  nearly  to 
the  eye-piece.  Bach  of  these  boards  is  furnished  with  a  pair  of  shutters  of  the  same  size,  which 
the  observer  can  turn  so  that  the  tube  of  the  telescope  shall  be  completely  enclosed  in  a  wooden 
hexagonal  prism,  or,  more  exactly,  a  frustmm  of  a  pyramid,  and  thus  protected  from  the  heat 
of  the  observer's  body. 

(8)  The  steps  for  reading  the  microscopes  need  no  explanation  except  that  a  hand-rail 
runs  along  the  platform,  by  which  the  observer  passes  from  one  side  of  the  pier  to  the  other, 
without  descending  to  the  floor. 

DETAILED  DESCRIFTIOM,  WITH  EXPLANATIONS  OF  THE  PLATES. 

(9)  Plate  I  is  a  plan  of  the  observing-room. 

Plate  II  is  a  section  of  the  walls  and  masonry  below  the  floor  in  the  plane  of  the  meridian 
of  the  instrument,  with  a  view  of  the  room  as  seen  from  the  west 

B  is  the  entrance  from  the  main  building.  It  is  dosed  by  two  doors.  The  floor  of  the 
room  being  thirty  inches  lower  than  that  of  the  main  building,  a  platform  and  flight  of  steps  is 
erected  inside  the  door  for  convenience  in  entering  the  room. 

(10)  Below  the  floor  all  the  masonry  is  of  rough  stone  set  in  lime  and  sand  mortar.  The 
base  of  the  masonry  rests  upon  the  ground  about  six  feet  below  the  flooring  joists. 

L  L  are  the  collimator  piers,  the  bases  being  of  masonry,  three  feet  square,  and  the  upper 
parts  octagonal  monoliths  of  marble. 

S  S  are  piers  which  support  the  turn-table,  T,  and  the  floor  of  the  room  under  the  in- 
strument. '  ' 

B,  plate  n,  shows  the  masonry  which  supports  the  circle  itself.  B  is  a  prism  of  the  ma- 
sonry already  described,  eleven  feet  from  east  to  west,  four  and  a  half  from  north  to  south,  and 


'   4MIHik4w«MMA<>*Wita 


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milTID  ITATia  HAYAL  OBSUTATOtT. 


1 


five  io  height.  lU  boricontal  diroensioos  are  therefore  only  tuffioient  to  support  the  great  piers 
of  the  inatrnment.  It  is  covered  by  a  solid  oap  Q,  Plate  II,  of  hard  bluok  stone,  of  the  same 
horiaontal  dimensioos,  and  about  one  foot  m  tbiokness. 

On  this  cap  rest  the  marble  piers  P,  P'.  Their  bases  are  Ijollowed  oat  ho  that  they  each 
reet  on  three  points,  and  thus  remain  secure  without  cement  or  other  fastening.  Their  great 
mass  insures  perfect  steadiness  without  such  aids.  0,  0,  show  how  the  inside  corners  of  the 
piers  are  cut  away.  The  concaye  faces  0,  0,  0,'0,  are  parts  of  the  surfaces  of  four  vertical  cyl< 
inders,  the  axes  of  which  are  in  the  plane  of  the  inside  face?  of  the  piers,  23^  inches  north  and 
south  of  the  middle,  and  therefore  47  inches  apart. 

The  perforation  through  each  pier,  at  the  end  of  the  axis  of  the  instrument,  is  shown  at 
0,  Plate  II. 

(11)  B,  B,  R,  B,  B,  R,  show  the  railroad  on  which  the  reversing  carriage  runs.  Under 
the  instrument  the  rails  rest  upon  two  strong  joists,  supported  by  the  piers  S  S.  The  turn- 
table T  revolves  on  six  cannon  balls.  By  it  the  reversing  carriage,  with  the  circle  on  it,  may 
be  run  into  either  the  northeast  or  the  northwest  corner  of  the  room.  The  turn  •table  is  not 
necessary  in  reversing,  as  the  T's  uf  the  reversing  carriage  themselves  revolve  on  a  pivot. 
The  whole  floor  is  on  the  same  levbl,  except  around  the  collimator  piers,  on  three  sides  of  which 
a  platform  is  built. 

(12)  Plate  IV  exhibits  »  i  nd  dlevation  of  the  instrument  from  the  south,  with  the  hanging 
level  and  so  much  of  the  reve-tiing  carriage  as  is  not  concealed  by  the  telescope.  The  ladders 
are  omitted. 

Plate  y  is  an  isoa.  ;'ic  side  elev>  ion  from  the  eaitt;  the  east  pier  with  its  appurtenances, 
the  step-ladders,  and  the  hanf   o^  level,  all  being  removed. 

(13)  a  is  a  movable  rt'  ji,  'or  supporting  a  lump  in  observing  the  nadir  poiut.  b,  b  are  the 
counterpoises  which  lighten  the  weight  of  the  instrument  upon  the  pivots.  The  levers  o,  o 
which  support  them  have  a  siigbt  movement  around  the  pivots  &,  d.  The  hooks  ,/*,  /  nave 
friction  rollers  at  the  bottom  for  supportiut^  most  of  the  weight  of  the  instrument.  At  the  top 
they  expand  into  a  strong  rectangular  frame,  throiu^h  which  the  ond  of  the  lever  c  paitsen,  as 
shown  at  o,  Plate  Y.  Through  the  top  of  th«i  frame  passes  the  screw  d^  the  lower  end  of 
which  being  rounded  off,  rests  in  a  socket  in  the  top  of  the  lever,  and  thus  supports  the  weight. 
Small  pieces  of  rubber  have  beeu  placed  in  these  sockets  and  under  the  supporting  screws, 
for  reasons  to  be  explained  hereafter.  When  the  instrument  is  raised  from  its  pivots  the 
counterpoises  are  supported  by  the  screws  e,  e,  which  are  adjusted  so  as  to  allow  a  small  play 
to  the  levers. 

(14)  Jfoitn/tngr  <tf  the  Microtoopea. — Enlarged  views  of  the  hollow  cylinder  D  with  its  attach- 
ments are  shown  in  Plate  YI.  The  portion  P  iaset  into  the  pier  with  plaster;  grooves  are  cat 
through  the  flanges  p,  p,  p  to,  let  the  plaster  run  through.  I  is  the  disk  to  whi<^h  the  microscope 
arms  are  fastened.  It  expands  in  thickness  toward  its  circumference.  The  portions  J  and  k 
of  the  microscope  arms  hold  the  disk  firmly  between  them,  being  held  together  by  means  of 
clamping  screws,  the  heads  of  which  are  shown  in  Fig.  1.  These  screws  pass  through^'  to  k,  just 
outside  the  edge  of  the  disk.  To  keep  j  in  position  when  these  screws  are  loosened,  it  is  fitted 
with  pins  which  fit  corresponding  holes  in  k.  By  loosening  the  screws  the  microscope  arms 
can  be  moved  independently  around  the  disk,  but  will  not  come  nearer  to  each  other  than 
about  48°. 

Outside  of  k,  the  microscope  arms  are  loosely  encased  in  mahogany  shields  I,  to  protect 
them  against  rapid  changes  of  temperature. 

The  outer  ends  of  the  arms  are  hollow,  holeb  about  f-inch  in  diameter  running  into  them, 
to  receive  the  holders  which  carry  the  microscope.  They  are  encircled  by  the  circular  clamps 
t,  which  are  tightened  by  means  of  the  screws  h,  partially  shown  in  Fig.  2,  but  hidden  by  the 


i 


1 


Kk  Ji 


^^m 


DESCRIPTION   OF  THE   TRANSIT  CIRCLE   OF  THE 


Tjr 


t4M( 


clatnpH  in  Fig,  1.  When  /♦  is  tightened,  the  microscope  is  firmly  held  by  the  arm.  By  loosen- 
ing it  the  microscope  may  be  drawn  out,  and  three  views,  as  thus  removed,  are  given  in  Plate 
VII,  Figs.  1,  2,  3,  each  of  which  is  from  a  position  at  right  angles  to  the  other  two. 

(15)  a  (Plate  VII)  in  the  solid  metallic  support  which  passes  into  and  is  held  by  the  micro* 
scope  arm,  as  already  described.  The  holders  b  and  the  circular  clamps  c,  enveloping  the  body 
of  the  microscope,  form  a  single  piece  with  a.  When  the  screws  d  are  loosened,  the  microscope 
can  be  moved  longitudinally,  and  the  end  e  carrying  the  object  glass  can  be  slid  into  or  out  of 
the  other  portion,  for  adjusting  the  focus,  and  the  angular  value  of  a  revolution  of  the  microme- 
ter. For  the  accurate  adjustment,  the  independent  clamp  y  is  used.  Loosening  d  and  tighten- 
ing y  by  means  of  the  screw  d,  a  fine  motion  is  given  the  microscope  by  turning  the  screw  c. 
The  head  of  this  screw  ic  kept  pressed  against  b  by  the  spiral  spring  ^  pressing  y  and  b  apart. 

(16)  0  is  a  perforated  reflector  for  throwing  light  on  the  divisions.  Its  reflecting  surface 
is  not  polished,  but  is  of  a  bright  white.  It  can  be  turned  in  any  direction  by  the  milled  head/, 
and  can  be  moved  longitudinally  by  loosening  the  clamp  g. 

k  \b  &  cylinder  of  white  felt,  extending  very  nearly  to  the  face  of  the  circle,  at  the  same 
time  keeping  out  stray  light  and  assisting  the  illumination  from  o. 

(17)  The  micrometer  screws  of  the  microscopes  revolve  with  the  head.  Instead  of  being 
attached  to  the  moving  frame  of  the  diaphragm,  they  screw  into  the  latter,  and  thus  give  it  a 
slow  motion  to  or  from  the  bead.  Each  revolution  of  the  microscope  micrometers  is  30"  in 
angular  measure  on  the  circle,  and  about  one  hundredth  of  an  inch  in  linear  measure  on  the 
screw ;  30"  on  the  circle  measuring  about  -jaT  ''^^^i  ^^^  image  of  the  divisions  is  magnified 
about  3.3  times  in  the  focus  of  the  microscopes.  The  face  of  the  circle  is  about  1.9  inches 
from  the  object  glass  and  the  micrometer  wires  about  8.3  inches. 

Each  microscope  micrometer  is  set  upon  the  image  of  the  division  by  a  pair  of  parallel 
spider  lines,  distant  from  10"  to  11".  Microscope  YII  is  also  supplied  with  two  extra  pair  of 
wires,  about  2'  on  each  side  of  the  original  pair,  for  the  convenient  measurement  of  consecutive 
divisions. 

The  micrometer  head  is  divided  into  thirty  second -spaces,  each  of  which  is  again  sub- 
divided by  a  shorter  line  to  half  seconds.  The  entire  revolutions  are  read  from  the  interior  by 
a  serrated  scale.  The  divided  drum  may  be  turned  on  the  axis  of  the  screw  by  simple  pressure, 
without  turning  either  the  screw  or  its  bearing. 

(18)  Supports  of  the  Pivots. — Referring  again  to  Plate  VI,  the  cylinder  D  is  hollow  to  the 
depth  of  about  an  inch,  the  external  part  in  fact  consisting  of  a  rim  about  an  inch  thick.  The 
cylindrical  space  forming  the  interior  of  this  rim  contains  the  metallic  plate  e,  Fig.  1,  into  which 
screw  the  antagonistic  screws  8,  a,  the  beads  of  which  press  against  the  inside  of  the  rim.  The 
top  and  bottom  of  this  plate  are  bevelled  toward  the  pivot,  and  the  bevelled  edges  are  held  by 
the  plates  b,  b'.  When  the  screws  c,  c  are  loosened  the  plate  e  can  be  moved  from  right  to  left 
by  the  screws  s,  «,  but  when  they  («re  tightened,  e  is  firmly  held  between  the  plates  6,  b'. 

The  view  actually  given  is  that  of  the  west  plate,  by  which  the  axis  is  adjusted  in  azimuth. 
The  east  one  is  similar,  except  that  the  plates  and  screws  are  turned  90°  for  adjusting  the  level. 

n  is  a  thin  perforated  plate  of  metal  which  presses  against  the  end  of  the  pivot,  to  prevent 
longitudinal  motion  of  the  axis.  As  now  arranged  for  observation,  the  eastern  one  is  firmly 
screwed  against  the  V  plate,  while  the  western  one  is  pressed  against  the  pivot  b}'  a  spring 
behind  it. 

The  V's  are  carried  in  the  rounded  plate  y,  which  forms  one  piece  with  the  plate  c.  They 
consist  simply  of  small  pieces  of  soft  metal  v  v,  (Fig.  4,)  slightly  convex  on  their  upper  surfaces, 
so  that  only  a  single  point  of  each  pivot  at  first  rests  upon  them.  But  a  slight  hollow  is  soon 
worn  into  each  of  them  by  the  pivot. 


"h"^^ 


UNTTKO  STATES  RATAL  OBSBBYATOBT. 


J 


(19)  The  Tdeacope  and  ita  External  Appendage*. — Betnrning  to  Plates  lY  and  Y,  and  para* 
ing  from  the  Y'b,  we  first  have  the  pivots,  which  are  2.1  inches  in  diameter,  and  1.8  inch  in 
length,  and  are  apparently  of  the  same  diameter  throughout  their  length. 

(20)  Next  to  the  pivots  the  axis  expands  into  the  frustrum  of  a  coue,  the  diameters  of  the  bases 
of  which  are  somewhere  about  three  and  a  half  and  four  and  a  half  inches,  respectively,  and  the 
height  about  three  inches.  Back  of  this  frustrum  the  axis  again  expands  perpendicularly  to  ita 
length.  Over  these  frustrums  the  circles  C,  0  fit  with  great  nicety;  the  central  perforations  in 
the  latter  being  tightly  filled  by  the  former  when  the  circles  are  pressed  against  the  expansion 
at  their  bases.  The  thickness  of  the  circle  is  slightly  greater  than  the  depth  of  the  frustum, 
so  that  the  latter  does  not  pass  quite  through  the  perforation.  The  circle  is  held  in  its  place 
by  the  friction  of  the  plates  p,  p  which  are  pressed  against  it  by  the  screws  a,  a,  a,  a, «,  (Plate  Y) 
passing  through  them  and  into  the  top  of  the  frustrum,  without  touching  the  circle.  When  these 
screws  are  loos^ened,  the  circle  can  be  turned  round  so  as  to  take  any  desired  position  relatively 
to  the  telescope. 

(21)  The  circles  each  appear  to  be  cast  in  a  single  piece.  The  manner  in  which  they  are 
stiffened  can  be  seen  by  a  comparison  of  Plates  lY  and  Y.  The  middle  of  the  plane  face  of 
each  circumference  is  inlaid  with  a  band  of  silver  on  which  the  divisions  are  cut  to  every  two 
minutes.  The  breadth  of  each  division  as  seen  under  the  microscope  seems  to  be  between  two 
and  three  seconds,  corresponding  to  a  thickness  of  about  7^  of  an  inch. 

The  circle  next  to  the  clamp  has  also  a  coarse  division  to  every  ten  minutes,  for  setting 
the  telescope. 

(22)  Next  to  the  circles  come,  on  one  end  of  the  axis,  the  clamp  n,  and  on  the  other  end 
a  ring  to  counterbalance  it,  into  which  screw  four  handles  A,  h  for  turning  the  telescope  on  its 
axis.  The  clamp  is  tightened  by  means  of  the  screw  q,  q,  (Plate  Y,)  and  a  slow  motion  may 
then  be  given  the  telescope  by  another  screw,  not  shown  in  the  figure. 

(23)  The  friction  rollers  are  received  by  grooves  cut  around  the  axis. 

On  the  clamp  end  of  the  axis  four  curved  handles  A',  V  (Plate  lY)  are  screwed  into  the  cone 
for  turning  the  telescope. 

Near  the  base  of  the  cone  flat  bands  are  seen,  by  which  the  instrument  is  supported  when 
on  the  reversing  carriage. 

(24)  The  central  cube  is  16  inches  square,  and  forms  a  single  piece  with  the  axis.  Its  sides 
are  perforated  in  a  direction  perpendicular  to  the  telest-ope  and  the  axis,  by  openings  2^  inches 
in  diameter,  through  which  light  can  pass  from  one  collimator  to  the  other.  They  are  closed 
by  covers  which  screw  into  them. 

The  tubes  of  the  telesi  ope  are  each  fastened  to  the  cube  by  sixteen  screws,  as  shown  in 
Plate  lY. 

(25)  The  Eye-piece. — Three  views  of  the  eye-piece  and  its  appendages  are  given  in  Plate 
YIII.  From  Figures  2  and  3  it  will  be  seen  that  there  are  six  8<)ries  or  strata  of  plates  in  the 
eye-piece.  The  first  or  outside  stratum,  of  which  a  face  view  can  be  seen  in  Fig.  I,  carries 
the  ocular  a  and  the  slide  for  giving  it  a  horizontal  movement  by  means  of  the  rack  work  and 
milled  head  b. 

The  second  stratum  consists  of  the  slide  and  fixed  guides  for  giving  a  vertical  aiiovement 
to  the  whole  of  the  first  plate,  with  its  guides  and  slide,  by  the  milled  head  c. 

(26)  The  third  stratnpa  consists  of  the  declination  micrometer  plate  with  its  guides.  A 
portion  of  its  outside  surface  is  seen  at  of,  d,  d,  d,  Fig.  1 .  e  is  a  fixed  index  for  reading  the 
approximate  position  of  the  plate  in  micrometer  revolutions.  /  is  an  opening  in  the  plate  to 
admit  of  the  free  passage  of  e.     An  opening  about  two  inches  square  is  cut  in  the  middle  of 


■« 


f^m 


e 


DB80BIPTI0N  OF  THE  TBAN8IT  OIBOLB  OT  THK 


61 

m 


the  plate,  and  across  this  opening  on  the  posterior  sarfaoe  of  the  plate  are  stretched  the  hori* 
zontal  spider  Hues  for  zenith  distance  observations  with  the  micrometer.  From  Fig.  3  it  will 
be  seen  that  the  micrometer  plate  d  carries  the  falcram  of  the  milled  head  o  by  which  the 
ocular  is  moved  vertically.  Consequently,  when  the  micrometer  is  moved,  the  ocalar  is  carried 
with  it,  and  the  movable  spider  lines  are  thus  kept  in  the  middle  of  the  field  without  touching  c. 

(27)  The  fourth  plate  is  moved  in  right  adcension  by  the  micrometer  head  B.  It  has  a 
rectangular  opening  like  Plate  III,  and  across  this  opening,  on  the  anterior  surface  of  the  plate, 
is  stretched  a  single  vertical  spider  line. 

(28)  The  fifth  plate  carries  the  fixed  spider  lines.  These  are  stretched  across  the  anterior 
surface  of  a  thin  annnlns  about  1^  inch  in  diameter,  which  projects  from  the  surface  of  the  fifth 
plate  by  an  amount  equi !  to  the  thickness  of  the  fourth  plate,  passing  through  the  rectangular 
perforation  in  the  latter.  Thus,  the  three  sets  of  spider  lines  are  sensibly  in  the  same  plane. 
The  entire  plate  can  be  moved  horizontally  by  the  three  antagonistic  screws  g  hg,  to  adjust 
the  line  of  collimation.  The  plate  is  fastened  to  the  piece  through  which  the  screws  pass  by 
the  projection  t. 

The  sixth  plate  forms  the  basis  for  all  the  rest,  and  is  pierced  for  the  holes  in  which  the 
micrometer  screws  turn.  It  is  fastened  to  the  eye-tube  E  by  a  cylinder  which  slides  tightly 
into  E,  and  is  fastened  by  the  six  screws  k. 

,.  (29)  The  Uterometer  Movements. — In  all  the  micrometers  of  this  instrument  the  screws 
revolve  with  the  heads.  In  the  microscope  micrometers  the  bearings  of  the  heads  are  fixed, 
and  the  screws  passing  into  the  movable  plates  draw  them  toward  the  micrometer  heads  as  the 
screws  turn  forward.  But  in  the  eye-piece  the  female  screws  are  bored  into  the  sixth  plate,  and 
the  bearings  of  the  heads  move  with  the  micrometer  plate.  The  projection  d  of  the  senith  dis- 
tance  micrometer  plate  is  attached  to  a  cross  n,  n,  n,(Fig.  3)  through  a  circularr^be  opening  in  the 
centre  of  which  the  micrometer  screw  passes  freely,  and  on  which  it  presses.  Thus,  as  the  screw 
turns  forward,  the  screw,  the  micrometer  head,  n,  and  d  are  all  slowly  moved  downward.  Tho 
middle  n  is  the  index  from  which  the  fractions  of  a  revolution  are  read,  but  they  can  equally 
be  read  from  the  front  index,  a  is  one  of  two  spiral  springs  by  which  the  cross  is  kept  pressed 
against  the  micrometer  head,  and  made  to  follow  it  as  it  is  withdrawn. 

(30)  Rogers^  Sdf-regiMlering  Micrometer  Head. — ^The  zenith  distance  micrometer  head  is 
famished  with  the  self-register  invented  by  Mr.  Joseph  A.  Bogers,  and  described  in  the  Astro- 
nomische  Nachrichten,  No.  1493.  The  four  arms  o,  o',  o",  o"'  (Fig.  1)  are  movable  around  the 
same  centre  with  the  micrometer,  which  passes  through  openings  in  the  middle  of  them.  They 
are  held  to  the  micrometer  by  the  friction  of  elastic  bent  plates  which  surround  the  centre. 
Tims,  when  free,  they  move  with  the  micrometer  head;  but  when  held,  the  head  moves  past 
them.  One  end  of  each  terminates  exactly  with  the  radius  of  the  micrometer  head,  and  serves 
R8  an  index,  as  may  be  seen  in  Fig.  3.  The  other  end  projects  a  little  beyond  the  cylindrical 
surface  of  the  head,  and  may  be  held  by  notches  in  the  levers  1 1,  (Fig.  2.)  When  thus  held, 
the  index  ends  are  in  the  same  vertical  line  with  the  principal  fixed  index,  as  shown  in  Fig.  3. 

The  mode  of  operation  is  as  follows :  The  micrometer  being  in  any  position  which  it  is 
desired  to  register,  one  of  the  levers  (Figs.  1  and  2)  is  moved  back  with  the  finger  to  the 
position  l\  and  the  movable  index  is  thus  set  free.  It  now  moves  round  with  the  micrometer, 
and  thus  points  continually  at  the  reading  indicated  when  it  was  set  free.  Four  successive 
readings  may  thus  be  registered  in  succession  without  taking  the  eye  from  the  telescope. 

The  object  of  the  two  extra  divided  cylinders  on  the  micrometer  head  is  simply  to  facilitate 
the  reading  of  the  four  movable  indexes. 


UinrBO  STATES  HATAL  0B8BBVAT0BT. 


(31)  The  Oculara. — The  instnimeDt  n  ftimished  with  five  oonlan,  of  which  the  in«gnifyiDg 
powers  are,  approximately — 


No.  1. 

ISO; 

8, 

160; 

3. 

180; 

4. 

260; 

6, 

360. 

No.  3  18  that  hitherto  most  used  in  aslronomioal  observations. 

(32)  The  Retiotde. — ^The  fixed  vertical  spider  lines  are  twenty-three  in  number,  arranged 
as  in  Fig.  4.  Seven  of  these  are  at  eqnal  intervals  of  12^  seconds  of  time,  and  are  designated 
by  the  Roman  nnmerals  I-VII.  For  convenience,  a  second  notation  is  adopted,  as  shown  at 
the  bottom  of  the  figare,  the  wires  being  divided  into  five  groups  A  to  E,  and  the  wires  of 
each  group  designated  by  subscript  Arabic  numerals.  Thus  the  wires  II,  III,  IV,  T,  and  YI 
are  designated  indiflferently  by  these  numbers  or  by  the  symbols  A„  B|,  G,,  D„  Ep  The  wires 
of  set  G  are  24.  apart ;  those  of  B  and  D  It, 5  and  2«.6  respectively.  Sets  A  and  E  are  rarely 
used.  Stars  are  usually  observed  in  right  ascension  ^ver  B  D  and  the  three  middle  wires  of  0. 
In  observations  of  planets  one  limb  is  observed  ove.  B  and  D,  the  other  over  C. 

The  middle  of  the  field  is  shown  by  a  single  pair  of  fixed  horizontal  wires  about  8"  apart. 
A  single  vertical  wire  is  moved  by  the  horizontal  micrometer. 

(33)  The  horizontal  movable  wires  consist  of  a  single  pair  4".6  apart,  between  which  objects 
are  usually  observed,  and  a  couple  of  single  wires  at  a  distance  of  ten  micrometer  revolutions 
on  each  side  of  the  central  pair.  The  former  were  inserted  by  the  machinist  of  the  observatory 
after  the  mounting  of  the  instrument,  in  lien  of  a  single  wire  inserted  by  the  makers. 

(34)  The  IttumincUion. — The  flames  of  the  two  lamps  L,  L,  Plate  lY,  are  nearly  surrounded, 
by  parabolic  reflectors.  The  light  passes  through  the  supporting  tube  and  the  pier  into  the  cyl- 
inder D;  here  it  meets  a  combination  of  lenses  and  prisms,  shown  in  Plate  YII,  Figs.  4  and  6. 
Fig.  4  gives  an  end  view  of  the  combination,  as  seen  from  the  lamp.  Fig.  5  gives  a  side  view. 
The  nearly  cylindrical  frustum  of  a  cone  G  is  pierced  in  the  direction  of  its  axis  by  five  holes, 
a,  b,  b,  b,  b.  The  light  which  enters  a  passes  through  two  lenses,  and  through  the  perforations 
in  the  pivots  of  the  instrument  to  the  centre  of  the  axis.  That  which  passes  through  the  b'a 
meets  four  prisms,  p,  p,  from  the  interior  surfaces  of  which  it  is  refiected  at  an  angle  of  about 
42^°,  BO  as  to  be  deflected  in  all  about  85°.  G  and  D  fit  snugly  in  a  perforation  in  the  centre 
of  the  cylinder  D,  Plate  lY;  a  hole  receives  the  pin  e,  and  thus  fixes  the  position  of  the  appa*. 
ratus.  The  latter  can  be  removed  by  unscrewing  the  lamp-tubes  T,  and  reaching  the  arm 
through  the  pier.  When  in  place,  its  position  is  such  that  the  light  reflected  from  the  prisms  p 
passes  down  the  pipes  k,  (Plate  lY,)  and  into  the  reflectors  of  the  microscopes,  by  which  it  is 
thrown  upon  the  divided  limb. 

(35)  The  central  ray,  passing  {ihrough  a,  if  it  enters  the  clamp  end  of  the  axis,  is  conducted 
to  four  prisms  in  the  central  tube  of  the  axis,  from  which  it  is  reflected  down  the  side  of  the 
tube  to  four  more  prisms  in  the  eye-piece,  and  thence  to  the  wires,  in  the  usual  way.  Thus 
the  wires  may  be  iUuminate<lf.  or  darkened  by  turning  a  milled  head  on  the  clamp  side  of  the 
eye- piece. 

(36)  The  light  which  enters  the  other  end  of  the  axis  is  reflected  from  a  prism  about  4^ 
inches  from  the  centre  of  the  axis,  directly  to  the  eye-piece.  It  shows  the  dark  wires  on  the 
bright  field.  It  may  be  changed  in  color  from  yellow  to  blue,  or  cut  off  entirely  by  turning  a 
milled  head  on  the  side  of  the  tye-piece  opposite  the  clamp. 

(37)  The  CoRimaiora. — Fig.  6,  Plate  YII,  gives  a  general  view  of  each  collimator.  The 
object  glasses  have  each  2|  inches  clear  aperture,  and  35  inches  focal  length.     The  eye-piece 


8 


DBSORIPnON  OF  THB  TBAN8XT  OIBOLB  OF  THX  D.  8.  NAVAL  0B8BBVAT0BT. 


of  one,  which  is  designated  collimator  A,  is  fornished  with  a  pur  of  parallel  wires,  ditit»nt 
about  9",  with  a  single  wire  crossing  them  at  right  angles.  The  wires  of  the  other,  called  col- 
limator  3,  form  a  simple  cross.  When  it  is  required  to  .set  the  collimators  opposite  each  other, 
the  coincidence  is  that  of  a  single  wire  of  B  with  the  mean  of  the  parallel  wires  of  A. 

The  steel  plate  which  carries  the  wires  is  held  between  four  antagonistic  screws,  but  has 
no  binding  screws. 

The  supporting  collars  of  the  collimators  are  only  23  inches  apart,  so  that  each  end  of  the 
collimators  projects  about  six  inches  from  its  support. 

Each  collimator  is  furnished  with  a  delicate  spirit  level,  which  sets  on  the  supporting  collars. 

(38)  The  Ts  of  the  collimators,  with  the  way  in  which  they  are  fastened  to  the  piers,  is 
shown  in  Figs.  7  und  8.  The  hemispherical  bottoms  of  the  screws  a,  a,  a,  rest  in  three  cavities 
in  a  Y-shaped  block  of  metal,  which  is  set  into  the  pier  with  plaster.  The  outline  of  the  block 
is  shown  by  the  dotted  lines.  The  three  screws  6,  b,  b,  pass  centrally  through  a,  a,  and  thus 
bind  the  Y-plate  firmly  to  the  block.  The  level  of  either  pivot  is  adjusted  by  loosening  6,  and 
turning  a  to  the  required  extent.  The  azimuth  is  adjusted  by  the  antagonistic  screws  c,  e. 
When  the  V  is  in  position  it  is  bound  by  the  screws  d,  d,  e,  e. 


m 


PAKT  II. 


GENERAL  METHOD  OP  INVESTIQATINQ  THE  ERRORS  OP  A  TRANSIT  CIRCLE. 

(89)  The  most  important  and  •'iffioult  part  of  this  investigation  is  the  determination  of  the 
effect  of  gravity  in  changing  the  relative  positions  of  the  various  parts  of  the  instrnment,  and 
the  correction  of  observations  for  this  effect.  It  is  therefore  proposed  to  develop  a  general 
method  of  determining,  either  rigorously,  or  with  a  near  approach  to  rigor,  the  effect  of  gravity 
in  changing  results  of  the  various  observations  by  which  the  position  of  a  star  is  determined. 

The  necessity  for  a  flexure  correction  may  be  regarded  as  an  imperfection  in  an  instru- 
ment, since,  if  it  were  well  balanced,  and  equally  elastic  in  all  its  parts,  no  such  correction 
would  ever  be  necessary.  Artists  generally  attempt  to  avoid  this  imperfection  by  distributing 
the  weight  of  the  instrument  so  that  it  shall  be  perfectly  symmetrical  with  respect  to  the  centre. 
Thus,  in  the  Washington  Transit  Circle,  the  two  circles  are  of  equal  weight;  the  clamp  is  coun- 
terpoised by  a  cylinder  at  an  equal  distance  on  the  other  end  of  the  axis;  and  the  tubes  of  the 
telescope  had  their  outer  and  inner  surfaces  turned  simultaneously,  in  order  to  secure  perfect 
equality  of  thickness  in  every  rectangular  section  of  the  tube.  Yet,  the  effect  of  irregular 
flexure  cannot,  by  any  means,  he  neglected,  and  that  of  the  two  circles  exhibits  a  very  sensible 
difference.  A  similar  remark  will  probably  apply  to  every  large  instrument  ever  made.  It 
will  not,  therefore,  do  to  assume  that  such  an  instrument  is  equally  elastic  in  any  of  its  corre- 
sponding parte,  however  unexceptionable  may  be  its  construction. 

(40)  The  only  arbitrary  hypothesis  we  shall  assume  respecting  any  law  of  elatitioity  in  the 
instrument  is,  that  the  relative  flexure  of  the  various  parts  is  the  same  as  if  the  instrument, 
during  a  revolution  on  its  axis,  were  always  supported  by  the  same  particles  of  its  mass. 
The  nature  and  the  results  of  this  hypothesis  will  be  rendered  more  clear  if  we  suppose  the 
instrument  to  remain  at  rest,  and  gravity,  with  the  forces  which  oppose  it,  to  act  in  various 
directions.  The  parts  of  the  instrument  which  sustain  these  opposing  forces  are  mainly  those 
which  press  on  the  friction  rollers  of  the  counterpoises.  Reflecting,  now,  that  the  direction  of 
these  forces  always  passes  within  two  or  three  inches  of  the  centre  of  the  axis,  and  that  our 
hypothesis  can  be  incorrect  only  by  a  combination  of  the  two  following  circumstances,  viz: 
l'  An  unequal  elasticity  in  the  parts  of  the  conical  axis  on  which  the  friction  rollers  succes- 
sively press;  2.  Such  a  relation  of  elasticities  in  other  parts  of  the  instrument  that  the  unequal 
elasticity  of  this  narro<v  band  on  the  conical  axis  causes  the  instrument  to  change  its  form  ac- 
cording to  a  different  law  from  that  which  would  hold  true  if  the  elasticity  of  the  band  were 
uniform — ^it  would  seam  that  the  hypothesis  must  be  a  safe  one. 

Experiment  shows  that  the  effect  on  elastic  bodies  of  forces  which  are  very  small  in  pro- 
portion to  the  rupturing  force  is  strictly  subject  to  the  law  of  superposition  of  small  motions; 
that  is,  that  the  combined  effect  of  several  such  forces  is  the  sum  of  the  effects  that  each  would 
produce  acting  separately. 


^■-mmmmmmm 


10 


DESOHIPnON  OF  THE  TBTMSIT  OIBOLB  OF  THK 


(41)  Still  snpposing  the  inatrament  fixed,  and  the  direction  of  gravity  variable,  let  b  rep- 
resent the  amonnt  by  which  a  point  of  the  inBtrument  is  moved  from  its  normal  position  in  the 
direction  of  an  arbitrary  fixed  axis  when  gravity  acts  in  the  direction  of  that  axis,  and  let  a  rep- 
resent the  displacement  in  the  same  direction  when  gravity  acts  at  an  angle  of  90°  with  the 
axis.  If  gravity  acts  at  an  angle  W  with  the  axis,  it  may  be  resolved  into  the  forces  g  cos  W 
and  g  sin  W,  acting  along  and  perpendicularly  to  the  axis.  The  first  component  will,  by  the  law 
just  referred  to,  produce  the  displacement  6  cos  W,  and  the  second  the  displacement  a  sin  W, 
and  the  whole  effect  of  gravity  will  be  a  sin  W-|-6  cos  W. 

Suppose,  then,  any  system  of  rectangular  co-ordinates  fixed  in  the  instrument,  and  revolv- 
ing with  it;  then,  as  the  instrument  revolves,  the  law  of  displacement  of  any  point  in  the  di- 
rection of  the  movable  co-ordinates  will  be  given  by  the  equations 

dx=a  sinW+b  cosW, 
iy=a'  Bin  W-\-f/  cob  W, 
*««sa"  Bin  W+i"  COB  W. 

W  being  the  angle  of  position  of  the  instrument,  and  a,  a',  a",  b,  6,'  6,"  constants,  to  be 
determined  by  observation. 

(4*2)  The  method  of  determining  such  of  these  constants  as  are  necessary  in  the  correction 
of  afltronomical  observations  will  next  be  shown.  To  admit  of  the  application  of  this  method  it 
is  necessary  that  the  instrument  ahculd  be  supplied  with  a  pair  of  collimators,  each  of  which 
admits  of  being  accurately  levelled,  in  order  that  it  may  be  used  to  determine  the  horizontal 
point,  and  an  artificial  horizon  for  observing  the  nadir  point  by  reflection  from  mercury.  A 
vertical  collimator,  to  be  fixed  over  the  centre  of  the  instrument,  and  set  vertical  ither  by  re- 
flection of  its  wires  from  the  mercury  bath,  or  by  levelling  its  axis,  would  also  be  valuable  as 
an  independent  check  on  some  of  thd  results. 

(43)  Let  us  now  consider  the  causes  which  will  affect  the  reading  of  any  microscope.  If 
the  divisions  are  truly  cut  in  direction — that  is,  if  each  stroke  is  sensibly  in  the  same  plane  with 
the  axis  of  the  circle,  the  error  of  each  point  in  any  one  division  may  be  regarded  as  the  same. 
We  shall  therefore  regard  the  diviftions  as  a  series  of  points.  When  a  microscope  is  read,  the 
position  of  the  point  under  the  microscope  is  determined  by  bringing  a  micrometer  wire  into 
coincidence  with  the  image  of  the  point  in.  the  microscope.  This  micrometer  wire  in  the  Ger- 
man instruments  is  an  imaginary  one  bisecting  the  space  between  two  real  ones.  The  division 
point  is  then  in  the  plane  which  passes  through  this  micrometer  wire  and  the  optical  centre  of 
the  object  glass  of  the  microscope.  Let  us  consider,  as  the  zero  of  the  micrometer  its  position 
when  the  plane  passing  through  the  object  glass  and  the  micrometer  wire  is  at  right  angles  to 
the  face  of  the  circle.  The  micrometer  reading  of  the  division  will  then  be  proportional  to  the 
ttingent  of  the  angle  which  the  plane  containing  the  division  makes  with  this  last  plane.  No 
appreciable  error  will  result  from  supposing  this  adjustment  to  be  perfect. 

The  subsequent  investigation  will  be  precisely  the  same  if  we  suppose  the  divisions  to 
radiate  from  the  centre  of  the  circle,  and  the  micrometer  wires  in  the  microscope  to  be  a  point, 
which  is  brought  into  coincidence  with  the  image  of  the  division.  The  micrometer  reading 
will  then  represent  the  tangent  of  the  angle  which  the  plane,  passing  through  the  centre  of  the 
object  glass  and  the  division,  makes  with  that  passing  through  the  centre  of  the  object  glass 
and  the  axis  of  the  circle. 

If  the  eight  microscopes  were  correctly  adjusted  in  position,  and  the  circles  perfect  in  form 
and  position,  and  not  acted  on  by  gravity,  the  instrument  might  be  so  set  that  all  the  micro- 
scopes should  read  zero  at  the  same  time.  The  following  include  all  possible  deviations  of  the 
circles  and  the  microscopes  from  this  state. 


URITET)  K'AnS  NATAL  OBURTATORT. 


11 


a.  Errora  in  the  Angtihr  PoMiont  of  tht  MRoro9Cope$. — When  all  the  microscope  micrometers 
are  set  at  zero,  the  planes  passing  through  the  micrometer  wires  and  the  centre  of  the  object 
glasses  onght  to  cut  the  line  of  divisions  at  points  making  angles  with  the  centre  of  the  axis 
equal  to  the  nominal  distance  of  the  microscopes. 

p.  Error$  m  the  Oeneral  PoaUixmt^  the  Cirtlte.—The»9  will  be  six  in  number:  small  motions 
of  translation  in  the  direotion  of  three  co-ordinate  axes,  and  small  motions  of  rotation  around 
those  axes.  * 

f.  Enron  in  the  Position  </  the  Divieion  on  the  Oirde. — ^These  may  be  three  in  number.  I. 
Errors  in  the  angular  position  of  the  division.  2.  Deviation  of  the  surface  on  which  the  divis* 
ions  are  cut  from  a  plane  cutting  the  axis  of  revolution  of  the  instrument  at  ri|{ht  angles.  3. 
Change  in  the  position  of  the  division  produced  by  the  effect  of  gravity  on  the  circle. 

The  position  of  a  division  may  be  in  error  by  any  of  the  nine  causes,  ]9  and  y.  To  deter- 
mine their  effect,  let  us  refer  the  position  of  the  division  to  three  co-ordinate  axes,  those  of  X 
and  T  being  in  the  plane  of  the  circle,  and  that  of  Z  being  the  axis  of  revolution.  Let  A  be 
the  angle  which  the  plane  of  the  micrometer  wire  and  object  glass  makes  with  the  axis  of  the 
circle,  B  the  angle  of  position  of  the  microscope,  counted  from  the  axis  of  X. 

B,  the  radius  of  the  circle. 

c,  the  distance  of  the  centre  of  the  object  glass  from  the  plane  of  the  circle. 

r,  the  reading  of  a  microscope  from  its  own  zero. 

p,  the  mean  reading  of  a  pair  of  opposite  microscopes. 

m,  the  error  of  position  of  a  microscope. 

M,  the  mean  error  of  a  pair  of  opposite  microscopes. 

e,  the  error  of  division. 

t,  the  mean  error  of  a  pair  of  opposite  divisions,  or  an  error  in  iue  position  of  a  diameter. 

a,  b,  the  flexure  coefficients  of  any  point  of  the  circle. 

a,  /9,  half  the  difference  of  a  or  b  for  two  opposite  points  of  the  circle. 

£,  17,  the  possible  motions  of  translation  of  the  centre  of  the  circle  relatively  to  X  and  Y. 

at,  the  error  of  pointing  of  the  telescope. 

The  differential  coefficient  of  tan  A,  (which  is  proportional  to  r)  with  respect  to  the  co- 
ordinates of  the  division,  will  then  be: 


<2.tanA    B.ir 
dm     °*c<te 

SinB 

<2.UnA    Bir 

cosB 

c     ' 

<itanA    Edr 
dz         cdy 

tanA 
e 

The  effect  of  small  changes  dx  iy  and  dz  on  the  reading  of  a  microscope  will  therefore  be 

dr=:--8inB^-fco«B^+tanA^.    (1) 

Changes  in  the  co-ordinate  z  can  arise  only  from  a  motion  of  translation  of  the  instrument 
in  the  direction  of  its  axis;  from  motions  of  rotation  around  the  axis  of  X  or  of  Y,  in  consequence 
of  irregularity  of  pivots;  from  deviation  of  the  circle  from  a  plane  cutting  the  axis  at  right 
angles ;  or  from  lateral  flexure  of  the  circle.  If  the  effect  of  any  of  these  causes  is  appreciable, 
9z  must  be  determined  by  direct  measurement,  independently  of  the  readings  of  the  micro- 


mmsmsssmsmsm 


12 


DEBORIPnOM  or  THB  TBAMBIT  OIBOLI  OF  THB 


% 

«; 


Bcopes,  and  the  latter  mast  be  oorreotfid  accordingly.     To  jadge  when  d»  can  be  senBible,  we 
remark  that  in  general 


tanAi 


Bf->-+eonitaiiti 


the  constant  being  the  valne  of  tan  A  when  the  micrometer  reads  aero,  and  therefore  depend- 
ing on  the  parallelism  of  the  microscope  to  the  axis  of  the  circle.    If  the  changes  in  r  do  not 

R 
exceed  10"  and  -  does  not  exceed  12,  A  will  not  differ  more  than  1'  from  ito  mean  valne  in  a 

aeries  of  readings.  Since,  by  proper  adjustment,  this  mean  valne  may  be  made  ver>  small, 
there  is  no  necessity  that  A  should  ever  exceed  1'  in  a  aeries  of  measures.  In  this  case,  s  will 
have  to  change  by  -y^  the  radius  of  the  circle  to  produce  a  change  of  0".  1  in  r.  This  change 
being  ten  times  as  great  as  any  that  a  well  made  instrument  need  be  liable  to,  the  last  term  in 
ir  may  be  regarded  as  insensible,  if  the  microscopes  are  carefully  adjusted.  This  will  dispose 
of  four  of  the  nine  causes  which  may  affect  the  relative  position  of  the  divifipp ,  and  object 
glass.     The  remaining  five  will  be  included  in  the  equations  of  condition.  > 

Every  micrometer  reading  will  then,  by  equation  (1),  give  an  equation  of  the  form 


r«M-g  tin  B+l  COS  B+a  cos  B+ft  sin  B+e+i*. 


(«) 


(44)  The  problem  now  is  to  make  such  mechanical  arrangements  and  such  readings,  that 
from  a  series  of  equations  of  this  form  we  may  be  able  to  determine  the  values  of  the  coefficients 
in  thejiecond  member,  so  far  as  it  may  be  necessary  for  the  correction  of  observed  senith  dis- 
tances. To  obtain  a  complete  correction  for  the  readings  of  a  single  microscope  world  require 
the  solution  of  equations  of  extreme  complexity ;  we  shall,  therefore,  hereafter  consider  the 
corrections  of  a  pair  of  oppos  te  microscopes.  If,  now,  another  microscope  be  placed  at  the 
angle  180°-|-B,  and  its  reading,  taken  simultaneously  with  (2,)  be  indicated  by  an  accent,  we 
shall  have 

r'«m'+- sin  B-l  ooB  B-a' eos  B-»' sin  B-(-e'+». 
r  It 

Adding  this  equation  to  (2),  and  observing  that  by  the  rotation  already  given 

r  -I-  r'as8/», 

a  — a'aeSa, 
6  -  VnmSfi, 
e  +  tfasit, 

we  shall  have,  by  taking  the  mean  reading  of  a  pair  of  microscopes, 

/>=M+aeo8B-|-j^sinB-|-c-f«.  (3) 

an  equation  more  simple  than  (2)  and  equally  complete. 

(45)  The  mechanical  arrangements  necessary  for  the  proposed  method  are  these :  The 
instrument  must  be  furnished  with  two  finely  divided  circles,  each  read  by  four  microscopes. 
At  least  one  circle  must  be  capable  of  being  turned  on  the  axis  of  the  telescopp,  aqd  set  in 
any  required  position  relatively  to  the  telescope.  In  what  follows,  we  shall  sUppese  both 
circles  thus  movable.  The  microscopes  must  also  be  capable  of  being  set  at  different  angular 
positions.    The  details  of  the  arrangement,  and  the  mode  of  numbering  the  mioroaoopes  and 


■-  '¥^f-mm^'f-'jfim.fS^r^:  3?^CTa3Rtsa«»KW»««~^-  w»M?»»!t!<www^5""< 


UNITID  flTATIS  KATAL  OMIBTATOBT. 


li 


S$ulh 


counting  the  degrMs,  will  be  rappoied  to  correspond  to  thoee  of  the  Wwhington  transit 

circle.     The  Accompanying  diagram  shows  the  arrangements  referred  to,  as  seen  from  the 

west.    The  oater  circle  represents  the  westernmost 

one,  and  shows  the  positions  of  microscopes  I  to 

lY,  which  are  on  the  west  pier.    The  inner  circle 

represents  the  eastern  one,  and  shows  the  positions 

of  the  four  microscopes  V  to  VIII,  which  are  on  the 

east  pier.     The  arrows  point  in  the  direction  in 

which  the  degrees,  as  nnmbered  on  each  circle, 

increase.     It  will  be  seen  that  the  two  circles  are   ^orth 

divided  in  opposite  directions,  so  that  when  the 

instmment  is  reversed  the  circle  now  east  will  read 

in  the  same  direction  as  the  former  one,  and  so  for 

the  west.    Also,  as  the  instmment  is  turned  in  any 

direction,  the  snm  of  the  readings  of  any  microscope 

on  the  west  pier  and  any  microscope  on  the  east  pier  ^ 

will  be  a  constant  depending  on  the  relative  posi*  sj 

tions  of  the  circles. 

We  shall  suppose  the  axis  of  X  to  pass  in  the  direction  of  microscopes  I-ni,  and  that  of 
Y  in  the  direction  of  II-IV.    Thns,  we  have  for  microscopes 

I  and  VIII.  B=180O} 

II  sad  VII,  B«  90O; 

III  sod     VI,  B=    OO; 

IV  and      V,  B«270O. 

(46)  The  flexnre  effect  which  it  is  required  to  determine  is  the  change  in  the  relative  di« 
rection  of  two  lines,  namely,  the  line  joining  the  object  glass  and  eye-piece  micrometer  of  the 
telescope,  and  that  joining  any  pair  of  opposite  divisions  which  chance  to  be  under  a  pair  of 
microscopes.  This  will  be  determined  by  finding  the  change  of  direction  of  each  line  relatively 
to  that  part  of  the  central  axis  to  which  the  circle  is  fastened.  The  total  flexure  will  therefore 
be  divided  into  two  parts:  1.  The  flexure  of  the  central  axis  relatively  to  the  ends  of  the  tele- 
scope. 2.  The  flexnre  of  the  diameters  of  the  circle  relatively  to  the  centre.  The  coefficients 
of  the  first  flexure  we  shall  represent  by  /  and  g  for  the  east  circle,  and  by  /  and  g*  for  the 
west  one.  Suppose,  then,  that  the  line  joining  the  object  glass  and  eye-piece  revolves  uni- 
formly; that  part  of  the  axis  which  passes  through  the  circle  and  holds  it  by  pressure  may 
be  affected  with  an  inequality  of  the  form 

/rinZ+^eosZ. 

Again,  supposing  this  part  of  the  axis  to  revolve  uniformly,  it  is  possible  that  a  diameter 
of  the  circle  may  be  affected  with  an  inequality  of  the  form 

a8tnC4>i9eos(, 

a  and  ^  being  coefficients  to  be  determined  separately  for  each  pair  of  divisions,  and  (  being 
the  angle  <^  position  of  the  diameter  counted  from  an  arbitrary  axis.  On  the  east  circle  we  shall 
for  convenience,  count  C  from  microscope  VI  through  V,  VIII,  and  VII,  and  on  the  west  circle 
from  microscope  II  through  I,  IV,  and  IIL  Then,  when  any  division  D  comes  under  microscope 
V,  the  mean  reading  of  V  and  VII  will,  by  the  effect  of  gravity,  be  increased  by  the  quantity 

«J>. 
When  the  same  division  comes  under  VI,  the  mean  reading  of  microscopes  VI  and  VIII  will 
be  increased  by  the  quantity 


uiuHiiiMmiiiiiiiiiiiiw 


u 


DKSCBIPTIOR  or  THB  TBAMSIT  OIBOUi  OF  THE 


,.T>. 

Tba  Mme  stotement  will  apply  to  the  we«t  drole  by  dimioishing  the  nnmber  of  the  mioro- 
•cope  by  lY,  to  that  ti.H  and  ^.D  will  be  the  flexare  when  the  diviiion  D  comes  under  mioro- 
icopea  I  and  II. 

Since  changing  ^  by  180°  la  the  same  as  changing  the  algebraic  sign  of  a  and  ^,  we  have 

a.(D-fl80O)»-a.D, 
;9.(D+l80O)«.-/J.D. 
In  equation  (3)  we  hereafter  substitute  for  a  cos  B-f-^  sin  B  the  two  floxnrea 

/■in  Z-\-g  OM  O+a  sin  C+Z*  eos  C 

Let  us  now  take  four  divisions  on  each  circle,  such  that  they  may  all  be  under  the  micro- 
scopes at  once.  Represent  them  by  a,  ft,  o,  d  on  the  east  circle,  and  a',  V,  cf,  d'  on  the  west 
circle,  the  lettering  being  in  the  same  direction  with  the  numbering  of  the  degrees,  and  of  the 
microscopes.     We  then  have 

cascca  error  of  position  of  line  joining  a—e, 

a.a^  error  of  flexure  of  a—c  when  under  mierosoc^  V. 

p.a=  error  of  flexure  of  a— e  when  nnder  mieroseope  VI. 

Suppose,  also,  that  when  a  is  under  niicroscope  V,  of  is  under  microscope  I.    Also  put 

/sin  Z+j-  eos  Z=/  *.— /.  («+180O), 

-/  sin  Z+^  eos  Zax/je.—/.  («+  ISQO), 
and  let 

Zo.    ^+900,    Z«4-180O,    Z,+270O 

be  the  four  zenith  distances  of  the  telescope  toward  the  south  when  the  divisions  are  brought 
successively  under  the  four  microeoopes.  Bepresent  by  fin.»  the  mean  readings  of  a  pair  of 
opposite  microscopes.     Then  we  have  the  following  equations  of  the  form  (3): 

First  position  of  telescope  Z^ 
^5.0=:M|+(.a+/jr»-|-a.a+«»,n.  />1.0aiMi+('ui-4-  /'jst+a'ui— •.0, 

Second  position,  2^+90*. 
/>fi.90=M,-|-c.i+/.(ire+90O)+a.6+«.90,        />1.90»M,-f<'.<{+/'.(«k+90O)+a'.<I— «.90. 
/>6.90=M«+<.e  +/(«^+90O)+i'-e+»-90,        />8.90asMt+«'.a4-/'.(««+00O)+/»'.a-«.90. 

Third  position,  Z.+ISO^'.  . 

/.6.180s=M,+«.c +/(«,+ 180O)+a.c-|-«».180,       /jl.lSO-Mj+t'x +/'.(««+ 180O)+a'.c  --.ISO, 
/>6.180sM,-f(.<2+/(««+i80O)+/}.i{+«.180,       /»8.180xsM«+t'.<{4-/'.(«k+^80O)+^.<2-<».180. 

Fourth  position,  S^+270°. 

/.6J870«M,+«.<l+/(«o+2700)4.a^+»^70.       ^lJ70=|li+«'.*+/'.(»o+8700)+«'A-»^70, 

/.6JB70asM,+t.c+/.(««+870O)+/9.a+*.270,       />2.870»M,+«'x  +/'.(«»+870O)+/!'jj  -i»J870. 

(47)  For  perspicuity,  let  na  reoapitalate  the  adopted  notation,  by  ezphiinii^  the  meaning 
of  the  i^ve  equations. 

If  l^ere  were  no  errors  of  division  or  adjostoMnt,  and  no  elasUdty  of  the  parte  of  the  in< 
stmment,  the  readings  of  all  the  microscopes  wonid  be  sero.  The  readings  not  being  aero,  and 
/>6.0  being  the  mean  reading  of  microscopes  Y  and  YII  ^hen  the  telescope  poiattf  approzi* 
mately  at  zenith  distance  Z^  the  first  equation  indicatri  that  this  value  of  />6.0  is  due  to  the 
five  following  causes: 

1.  Error  of  position  of  the  microscopes  Y  and  YII,  (M,.) 


ihmm 


nvimmmm 


tmrrwD  arAnt  mawml  oBsnTAioiT.  U 

5.  Brrora  of  the  divitioos  a  and  o  which  we  ooder  thete  miorotoopee,  (t.o.) 

8.  RoUtion  of  the  sxis  of  the  telesoope  reletively  to  iU  Hne  of  sight,  in  consequence  of 
the  irregolar  effect  of  gravity,  (Av) 

4.  Angular  change  of  Hne  joining  divuiona  a  and  o  relatively  to  axis  of  rotation  from  the 
same  cause,  (a.a.) 

6.  Incorrect  setting  of  the  telescope,  («.0.) 

In  any  one  of  the  above  fonr  positions  take  the  snm  of  />,  or  p„  and  /i^or  />,.  Take  alito  the 
corre»|K)nding  sum  in  a  position  of  the  circle  180**  .different,  then  subtrHCt  the  two  sums,  remern* 
bering  that 

/»— /(«+180O), 
•41  or/94iM— a.(a-f  180O)  or /».(a+180O), 
'.  f.a«Bt.(«+180O), 

and  call  the  difference  K,  using  the  notation 

K.ie.i— A>i.»-|-/»i.i— />i  («+180O)  — /»,.(i4- 180°). 

Put  also  g.K=/.n-^/.%  and  we  have  the  e^ations 

K.15.0mi2aM+W  a+2g  z,  K  lS.90xs     9a.b'-'2a'.b+^.{z+9(P), 

K.16.0»2/9.*+2o'.a+2^«,  K  10.90— 2a./9-2«'.A+2f  («+90O), 

K.26.0»B2a.o+2/9'.4+%.«,  K.26.90-     2a  5+2/J'.a+2f  .(«+90«>), 

K.26.0a,2liA+ail'*b+agje,  **          K.2e.90aB-2i9.a+2/9'4>-|-2^.(«+g0O). 

Of  these  eight  equations  it  will  be  seen  that  only  six  are  independent,  any  one  of  each  four 
being  identically  derivable  from  the  other  three. 

Now,  let  the  poeition  of  the  east  circle  on  the  axis  of  the  telescope  be  changed  by  180", 
and  let  the  same  divisions  be  again  read.  Treating  the  equations  derived  from  the  readings  in 
the  same  manner,  and  distinguishing  the  new  K's  by  an  accent,  we  shall  have 

KM6.0aB-8a.a+2o'4i+^.«,  KM6.90ss-2a.A-2«'.i+;^.(*+90O), 

K'M.0ss—2fii+2a'.a-^2g.»,  K'  16.90=     2fi.a-2a'.b+2g.{z+9(i°), 

K'.25.0ss:-2«  0+2/9'.*+^^.  K'J85.90»-2a.*+2/S'a+^.(«+90O), 

K'M.0=—2fiA+2^i+2gjK,  K'.S6.90s     2fiM+2fi'.a+2g.{z+9<P). 

Now,  turn  the  west  circle  180°  on  its  centre  and  again  repeat,  distinguishing  the  K's  by 
two  accents,  and  we  have 

K".16.0s»-2«.a— 2«'.a+ai^.«»  K'Mfi.90=r-2o.i-|-2a'.A+S!^.(«-|.90<'),  • 

K".16.0rB—2fi.b—2a'M-{-2gje,  K".16.90s:     2fi.a+2a'.b+2g.{zf9(P), 

K"MJ0sB^2a.a'-2fi'A+2g.z,  K".26.90sai—2a.b-'2^M+2g.{z+90O), 

K"J»6.0sB—2fib-2fi'.b+2g.z,  K".26.90=s     2/J.a-2/J'.a-»-^.(*-f-90«>). 

These  equations  suffice  to  give  two  values  of  each  of  the  required  quantities.  But,  to 
have  as  many  independent  determinations  as  possible,  a  fourth  series  of  readings  are  taken 
with  the  east  circle  restored  to  its  original  position.     We  then  have 

K"'.li.0a»2mM'-2afM+2ga,  K"M5.S!0»     2a.b+2afJb+2g.{+z9V>), 

K"'M.0ma»fiA^2»fM+2g.z,  K'".l6.90sM^2fiM+2afA+2g^z+0<P), 

K"'26  0^2aM-'2fi'b+2ga,  K'".86.90as    2*^—2^M+2g.{z+9(P). 

K"'MJ0ss2(t.b-2fi'.b+2g.z,  K'"M.90sm^2fi.a'-2/i'M+2g{z+W>). 

Adding  together  the  corresponding  equations  of  the  first  and  third  series,  and  also  those 
of  the  second  and  fourth,  we  shall  have 

^«sK.  10.O+KM5.OaBK.  16.U+K'M6.0»K.  2A.0+K".2fii0»K.  86.0+ K".  26.0 
!=KM«.0+K''M5.0»K.'16.0+K"'.l6.0=sK'.26.0+K."25.0s=K'.26.0+K'".86.0. 


i^ms^tmrxm^'sm 


If 


DMOUPTKM  or  TBI  nUMUT  OnOLB  OF  TBI 


*.» 


Of  these  eight  raliiec  only  nx  un  really  independent,  being  rabjeet  to  the  condition  thnt 
the  Bam  of  the  extreme  ynlaee  ie  eqaal  to  the  ram  of  the  meuit,  which  fhmiihea  »  check  on 
the  aconrecjr  of  the  compatntion. 

Again,  by  eimple  lobtraction  of  the  correeponding  eqaatione  in  iracceaaive  aeries,  we  find 
the  following  four  distinct  valnea  of  each  of  the  eight  qoantitiea  o^,  /9.a,  tuh,  fiJb,  af.a,  fi^jo^ 
af.b,  fif.b,  which  gire  the  circle  flexure. 


K  .lfi.O-K'  .15.0. 
K  JB0.O>K'  SA-O, 
K'".lfi.O-K"  .16.0, 
K'".««.0-K"  .85.0. 

K  .Ifi.O-K'"  Ifi.O, 
K  .16.0-K"'.16.0, 
K'  .16.0-K'M6.0, 
K'  .16.0-K"  .16.0. 


KM6.90-K  .16.90. 
K' 26.90-K  .S6.90. 
K'M6.90-K"M6.90, 
K".S6.90-K'".86.90. 

4/9'.«» 
K  J0  9O-K"'JA.9O. 

K  J6.90-K"'.86.90, 

K'  .86.90-K"  J8S.90, 

K' .86.90 -K''J6.90. 


K  .16.90— KM6.90. 
K  .86.90-K' .86.90, 
K'"  1A.90-K".16.90, 
K'".8«.90-K".86.90. 

K"M6.90-K  .lAJO, 
K'"  16.90-K  .16.90, 
K"  .16.90-K'  .16.90, 
K"  .16.90-K'  .16.90. 


K  .16.0-K'  .160, 
K  JM.O-K'  M.0, 
K'".16.0-K"  .16.0. 
K"'.86.0-K»  .86.0. 

K  J6.0-K"'.S6.0, 
K  .86.0-K'".86.0, 
K'.86.0-K"J6.0. 
K'  .86.0-K"  .86.0. 


(48)  Thus,  the  flexure  of  the  circles,  in  so  far  as  it  affiects  the  mean  reading  of  any  pair  of 
opposite  microscopes,  and  the  relative  flexure  of  the  two  ends  of  the  axis,  are  completely  wnd 
rigorously  determined.  It  remains  to  determine  the  flexore  of  the  line  joining  the  eye  and 
object  end  of  the  telescope  relatively  to  the  axis  itself.     We  have  supposed,  for  brevity, 

and  have  shown  how  to  find  g.u,  and  therefore  /— ^,  and  g-{-f^.  The  coefficients  /  g,  f  g',  may 
DOW  be  found  separately  and  independently  by  observations  of  the  nadir  point  and  collimators. 
An  observation  of  a  levelled  collimator,  corrected  for  inequality  of  collimator  pivots,  diffisreuce 
of  latitude  of  circle  and  collimator,  aerial  refraction,  and  oollimation  error  of  the  collimator, 
shows  the  circle  reading  when  the  line  of  sight  of  the  telescope  is  truly  horiiontal.  The  coin* 
cidence  of  the  direct  and  refiected  images  of  the  zenith-distance  wires  shows  the  circle  reading 
when  the  telescope  is  truly  verticaL  When  these  readings  are  corrected  for  circle  flexure,  the 
horizontal  and  vertical  circle  readings  will  be  as  follows: 

Ewtdrala.  Wostdnl*. 

Bonth  horiiontal  reading,   0«4-/  O't—f 

North  horisontsl  resdiog,  0«— /  O't+f 

Nadir  reading,  0«-jr  C'^—g'. 

Cg  being  the  true  reading,  independent  of  flexure.  From  these  equations  the  values  of  0^  /, 
and  g,  tf^f,  and  g',  may  all  be  determined. 

The  values  of/  and  f  may  also  be  determined  independently  by  viewing  the  wires  of  one 
collimator  through  the  other,  and  making  the  horiiontal  wires  of  the  latter  coincide  with  the 
images  of  those  of  the  formeir.  If,  then,  the  micrometer  wires  of  the  telescope  be  set  sucoes* 
sively  upon  the  images  of  the  two  collimator  wires,  the  line  joining  its  object  glass  and  microm- 
eter wires  will  have  moved  accurately  through  the  space  of  180°,  while  the  circle  will  indicate 
a  motion  of  I80°d=2/.  The  agreement  of  the  two  values  of/  will  afford  a  check  upon  the  ao- 
curacy  of  the  collimator  determinations. 

(49)  One  precaution  is,  however,  indispensable  to  an  accurate  result  The  different  strata 
of  air  in  the  room  must  be  as  nearly  as  possible  of  the  same  temperature.  For,  if  there  be  any 
admixture  of  warm  and  cool  air,  the  former  will  ascend,  and  we  shall  thus  have  a  temperature 
increasing  with  the  height  If,  now,  this  increase  amount  to  one  degree  Fahrenheit  in  nine  feet, 
the  curvature  of  the  ray  will  be  equal  to  that  of  the  water  level,  so  that  it  would  never  leave 
the  earth. 


"■"•'*''***■*""■""■'■'' ""  '     — -ITT-  Kii.jjimf  in«iuii.iiii.i]iiininn-|inr— 


UJfinO  ITATM  HATAL  OBaBBYATOBY. 


It 


The  oonrae  of  the  rey  being  carved,  the  yalae  of/  obtaiDed  from  the  opposing  oollioDitori 
will  be  vitiated.  On  the  other  hand,  if  we  adopt  the  other  method,  there  is  always  a  possibility 
of  error  arising  from  irregalarities  or  nnoertaiu  differences  of  diameter  of  the  collimator  pivots, 
or  poaeible  flexure  of  some  part  of  the  collimator  itself.  However  /  is  determined,  the  obser- 
vations shoold  be  made  with  the  shntters  open,  and  under  atmospheric  conditions,  as  necrly  as 
praotioable,  like  those  nnder  which  the  astronomical  observations  are  made.  Considering  the 
difficulty  of  rigorously  fulfilling  this  condition,  it  would,  perhaps,  be  better  to  determine  /  by 
reflection  observations  of  stars,  g  also  admits  of  being  determined  by  a  comparison  of  North 
Polar  Distances  of  stars  near  the  zenith  in  reversed  positions  of  the  instrument. 

EBR0B8  OF  DiyiSION. 

(60)  The  method  of  determining  the  errors  of  division  is,  in  principle,  that  usually  adopted, 
the  operation  being  so  conducted  as  to  eliminate  all  irregular  flexure  of  the  circles. 

liOt  us  suppose  the  two  pairs  of  opposite  microscopes  set  at  the  distance  B,  the  angle  posi- 
tion of  the  flrst  pair  being  0°,  and  that  of  the  second  pair,  B.  Take  a  series  of  pairs  of  divis- 
ions at  the  distance  B,  and  let  these  divisions  be  successively  brought  under  two  pairs  of 
microscopes.    Then,  using  the  same  notation  as  in  §  (43), 

Mio.     I.  ri»wi+^-J-ai-»-«i-f-«»i, 


II.  niaiMt-|--^cosB stoB+OteosB-faiflinB-fck-t-wi. 

ni.  fi>-M— 3^--as4-«»-f  Ml, 

rV.  r4BM4— 4eosB-h-gsiaB— OtCOBB— i4B{nB-^«4-fi»i. 
Whence,  adding  the  odd  and  even  equations 

/>^2^sMt4-at  COS  B-H/S*  sin  B-f-«i-f- wf 
Turning  the  circles  through  the  distance  B,  we  shall  have 


(1) 


^<y»Mi.J-a,+.,+«,, 


Turning  again 


,<»>. 
'<?■ 


:M|-(-a3  cos  B-f-^3  sin  B-f  ts+coi. 


(«) 


Mi-J-a3-|-«j-f-«3. 
p^^sMr^a^  tM  B+fit  sin  B-(-C4+«»4. 


Let  2»  be  the  number  of  motions  necessary  to  bring  the  circle  back  to  its  first  position. 
Then,  the  (t+l)th  reading  will  have  brought  it  round  180°,  so  that  the  same  divisions  as  at 
first  will  be  under  the  microscopes.     The  readings  after  the  tth  will  then  give 

/.<j+^)=:Mt-ai+.i+«(i+l). 

/.<*+^)asM,-.a,cosB-A"inB+«,+«'(«+l). 
^<j+*)=Mi-«,4..,+«(i+8),  ^^5 

/•+2)^M,-«,  eoB  B-A •»»  B+t,+«(H  8). 


10  ■ 


ice., 


ace. 


i;i*ii:jii«i«»iiiiiiiiiiiiftiiii!8 


18 


UE8CBIPTI0N  OF  TQE  TRANSIT   CIRCLE   OF  THE 


'M 


Taking  the  suma  of  readings  in  opposite  positions  of  the  circle,  we  have 


Using  the  notation 


we  have 


Mt— Mi  +  Ci— Ci=rI.1.2, 

Ma— Mi+ca— ct=I*2.3, 

Mj— Mi+e4--(3=I.3.4, 

&c.«        &c.t        tee. 


(4) 


(fi) 


Taking  the  sum  of  the  entire  series  of  values  of  I,  and  dividing  by  their  number,  the 
c's  will  destroy  each  other,  and  we  shall  have 


Putting 

we  shall  have 


Mj^Mi:=-r-. 


J.1.2=:I.1.2-(tf,— Ml), 


(7) 


«4-C3=^.3.4,  (8) 

&».,        Ice. 

Thus,  where  one  e  is  known,  all  the  others  may  be  found  by  successive  addition  of  the 
differences  A.  If,  however,  the  number  t  is  considerable,  the  accidental  errors  of  the  various 
As  may  in  the  additions  become  considerable;  it  is  therefore  necessary  that  at  least  every  fifth 
c  in  each  series  be  corrected  by  the  results  of  another  series  in  which  the  value  of  t  shall  be 
less  than  in  the  series  in  question.  The  correction  will  be  really  applied  to  M',— M„  which 
will  thus  be  determined  independently  for  each  sub-series.  Suppose,  for  example,  that  in  a 
first  series  the  microscopes  are  at  the  distance  45°,  so  that  t==4.  The  preceding  formulte  will 
then  give 

t.ifi  —e.O     =4  .0.45, 

C.90  — C.46  ssJ.45.90,  (9) 

c.l35->c.90  r=:J.90.135, 

c.O     — c.lSffssJ.lSff.O. 


In  a  second  series,  let  the  microscopes  be  placed  at  the  distance  16°. 
then  give 

e.l5— c.O  ssJ.O.ld,  C.60— c.45s=J.45.60,     &c.; 

e.30— c.l5=J.15.30,  (.75— c.60=J.60.75,     &;c.; 

t.45— c.30=J.30.45,  c.90— (.75=^.75.90,     &;e. 

Adding  each  of  (10)  and  comparing  with  (9),  we  have 

■A  ,0.15+J.16.30+J.30.45=J  .0.45, 
J.46.60+J.60.76+J.75.90=J.46.90, 

&c.,        &c.,        &c. 


The  formulae  will 


(10) 


».*lip>.vn'-;9t^-'.-WS«;i'«,»riMP^>aiSr«'KS*^^ 


the 


UNITED  STATES  NAVAL  OBSBBVATOBT. 


19 


If  tbe  readings  were  perfect,  these  equations  ought  to  be  exactly  satisBed.    Not  being  satis- 
fied, the  difference  is  due  to  tbe  accidental  errors  of  the  readings.    Let  i  be  the  probable  error 
of  each  of  the  left-hand  ^^s,  «  that  of  the  right-hand  ones,  and  e  the  amount  of  the  discrepancy. 
The  most  probable  distribution  of  the  discrepancy  will  then  be, 
to  each  left-hand  A,  .  ^ 


and  to  each  right  hand  A, 


The  corrected  values  of  A  being  substituted  in  (10),  we  shall  have  a  series  from  which  the 
most  probable  values  of  f„  fu.  &c,,  may  be  found  by  successive  addition  from  any  arbitrarily 
assumed  value  of  «,. 

DETEBMINATION  OP  THE  EBEOES  OF  SPECIAL  DIVI8IONS.-PBOBABLE  ACCIDENTAL  EBBOB  OP 

ISOLATED  DIVISIONS. 

(51)  The  determination  of  the  error  of  each  separate  division  being  impracticable,  this 
question  arises:  What  is  the  probable  error  of  any  isolated  division  relatively  to  any  consider- 
able number  of  the  divisions  near  it?  Measuring  a  series  of  contiguous  spaces  on  any  part  of 
the  circle  we  have  the  data  for  answering  this  question.  These  measures  can  also  be  made 
aviilable  for  the  termination  of  the  special  divisions  used  in  observing  the  nadir  and  horizontal 
points,  or  any  special  star  the  position  of  which  is  required  with  a  high  degree  of  accuracy. 
The  method  of  treating  these  measures  is  as  follows:  -  .       • 

The  space  between  two  adjacent  divisions  being  very  nearly  four  revolutions  of  the  microm- 
eter,  let  the  measure  of  the  first,  second,  third,  Ac,  spaces  be 

4  rev.  4-di,        4  rev.  +«i»,  •      4  rev.  -i-«is.      &«• 
Represent  also  by  x  the  error  of  runs  of  the  microscope  in  four  revolutions,  and  by  e,,  e,,  Ac, 
the  errors  of  division.     Then  the  measures  give  the  series  of  equations 


(1) 


Here  we  have  n  equations  for  the  determination  of  n-|-2  unknown  quantities.  The  remain- 
ing two  equations  are  given  by  the  condition  that  the  sum  of  the  squares  of  the  errors  of  divi- 
sion  must  be  a  minimum.     We  thus  have 


A*   .        <fcl    ,      -  <*«••        A 


(8) 


(3) 


e  in  the  last  equation  representing  any  error  of  division  taken  at  pleasure.  Regarding  x  and  e 
as  independent  variables,  any  change  in  e  («  being  given)  will  cause  an  equal  change  in  all  the 
other  errors  of  division.     We  have,  therefore. 


and  therefore. 


^    <**»     *.« 


deM     , 
de 


«^-f  ei-|-  Ac.  •  .  .  -f-ejiasO. 


(*) 


wmmtm 


so 


DE8CKIPTI0N  OF  TBI  TRANSIT  OIBCLB,  ETC. 


ml 


This  eqnation,  united  with  the  equations  (1,)  will  enable  us  to  express  each  error  of  division 
in  terms  of  x.  Multiplying  the  first  of  equations  (1)  by  »,  the  second  by  n— 1,  the  third  by  n— 2, 
Ac,  and  adding,  remembering  that 

JSemiO, 

we  have  an  equation  which  gives  e^  in  terms  of  x.  By  using  the  proper  coefficients  of  elimi- 
nation,  we  have  each  of  the  other  errors  in  terms  of  x.  These  coefficients  are  indicated  in  the 
following  table,  in  which  each  column  is  to  be  read  downward,  in  connection  with  the  words 
Mi  the  left, 

To  express e^         «i  c^  en—1  m 

the  eoeffieient  of  ai       is    «  —1      —1    .  .  .  —1  ->1 

*  "  "  at       is    »— 1    »— I       — 2    .  .  .  —8  —2 

«  ••  «  oa       is    «— 2    »— 2    «— 2    ...  —8  —8 


m 


tip 


M 
U 


a.(>i-l)is  2  2  2    .  .  .     -(w-l) 

«  "  "  aji       is  1  1  1     .  .  .  1 

The  equations  thus  obtained  are  as  follows: 


-(•-1) 

— « 


•jn+l) 


2 


x+Hai+(n~-l)at+  ....  +a4i+(fi+l)A,a=:0, 


{n-2){n+iy 


2 


«—  ai+(fi— 1>8,+  ....  +a.»+(ii+l)«is=0, 


%S;^J  («-4)(ll+l) 

2 


X—  ai— 2a,+()i— 2)a3+  .  .  .  +an+{n+l)e,ssO, 


(6) 


2 


X—  fli— 2<i|— Sas—  ....  — iiaji+(fi+l)ejiassO. 


We  have  now  only  to  suppose  the  last  members  of  these  equations  to  be  accidental  errors, 
and  solve  by  least  squares.    This  solution  gives  for  the  eqnation  in  0, 


»{n+l)(n+2) 
6 


x+nai+2{n—l)at+2(n'-2)a3+  ....  +na.nssO. 


Having  thus  obtained  the  value  of  a;,  the  quantities  e^—%  ^t'^*  ^^'•i  ^^^  immediately  formed 
from  equations  (1.)  Thus,  when  we  have  e^  the  other  e's  are  formed  in  succession  by  the  adding 
on  of  successive  differences.    The  value  of  e^  may  be  obtained  from  the  equation 

formed  by  multiplying  the  first  member  of  (1)  li>y  n,  the  second  by  n — 1,  Ac,  and  adding  with 
reference  to  (4.)  But  the  most  ready  way  of  obtaining  all  the  e's  is  perhaps  by  forming  them 
from  e;,:=0,  and  then  subtracting  from  each  ci  them  the  mean  value  of  the  e's  thus  obtained. 
If  one  of  the  e's  is  known  by  the  methods  already  explained,  the  values  of  the  differences 
eg— e,,  Ac,  will  not  be  changed,  and  the  vulues  of  aU  the  other  errors  may  be  found  by  addition 
of  the  differences  to  this  known  value. 


m 


««« 


MMMW 


^■1 


PART  III. 


DETERMINATION  OP  THE   CONSTANTS  OP  THE  TRANSIT   CIRCLE  AND  ITS 

SUBSIDIARY  APPARATUS. 

« 

(62)  Valve  <f  me  divitum  <^  ike  Spirit  Lends. — It  will  be  remembered  that  there  are  three 
levels — one  striding  level  for  each  coUimatov,  and  a  hanging  level  for  the  axis  of  the  in  trament. 
The  former  are  distingmshed  by  the  letters  A  and  B. 

1865,  October  18.  The  old  moral  circle  was  turned  until  the  telescope  was  horizontal, 
and  the  collimator  levels  were  set  astride  of  the  telescope.  Microscopes  A  and  B  of  the  circle, 
and  the  two  ends  of  the  babble  of  the  level,  were  then  read  in  different  positions  of  the  tele* 
scope,  as  follows: 


IficA. 

lO&B. 

LOTdA. 

L«r«lB. 

S.«d. 

N.end. 

S.eiid. 

N.end. 

1     1$ 

It 

i. 

i. 

d. 

4. 

w«r.» 

70.8 

1&4 

«i.3 

18.6 

38.3 

64.8 

66.4 

1.1 

85.8 

1.6 

81.5 

7S.8 

77.9 

87. 6 

51.3 

97.6 

47.3 

M.4 

87.1 

8.3 

86.8 

3.0 

98.8 

75.1 

77.6 

86.6 

50.5 

96.4 

46.8 

6K.S 

67.8 

15.0 

38.1 

16.4 

36.8 

t  r^^'i 

66.8 

44.6 

96.5 

41.0 

81.8 

( 

flO.9 

63.4 

36.5 

18.6 

34.1 

14.8 

• 

49.7 

68.8 

60.0 

86.1 

46.0 

86.8 

\. 

71.0 

7a8 

83.8 

—     0.6 

81.4 

1.6 

a 

50.9 

68.8 

49.6 

96.5 

46.8 

86.0 

1 

68.8 

71.8 

86.7 

8.6 

84.3 

4.6 

5 

L59.9 

68.7 

37.8 

13.4 

34.0 

14.8 

Temperatnre  57°. 

Prom  tiie  observations  is  concluded — 

One  division  of  levd  Ab0".826. 
One  division  of  levd  B8sO".860. 

The  level  error  of  the  collimators  being  kept  quite  small,  rarely  no  great  as  3",  the  valae  of  one 
division, 

0".84, 
has  been  adopted  for  both  levels. 


*lWil|l!M'>IW>im'*l*WU#!gi 


w 


2S 


DESCRIPTION  OF  THE  TRANSIT  OIROLB  OF  THE 


1866,  November  21.    The  hanging  level  was  nnspended  from  the  telescope  of  the  Moral 
Circle,  and  the  following  readings  taken: 


Mie.A. 

IficB. 

Level. 

N.end. 

a  end. 

// 

// 

d. 

d. 

16.8 

81.1 

JSt.l 

84.5 

86.9 

31.8 

80.6 

78.3 

40.3 

46.1 

6.8 

67.8 

14.9 

19.4 

34.4 

86.3 

41.5 

46.1 

4.0 

66.9 

35.7 

40.6 

10.8 

61.1  68.1(7) 

90.8 

36.8 

16.4 

68.3 

84.8 

89.0 

S8.8 

74.9 

18.6 

83.8 

89.8 

81.8 

13.8 

17.8 

36.8 

88.8 

48.9 

47.7 

8.0 

64.1 

Temperature  53*^.     From  which  is  concluded 

One  divi8ion=0".872a0«.068.  * 

The  three  readings  preceding  the  last  seem  to  indicate  a  diminution  of  the  value  as  we 
r^pproach  the  end  of  the  scale,  but  the  diminution  is  no  greater  than  what  may  be  due  to  errors 
of  the  microscopes. 

(53)  Difference  of  ccUara  of  ooRimaiora, — It  is  requisite  that  we  know  the  difference  be< 
tween  the  true  level  of  the  axis  of  the  collimator  and  the  readings  of  the  spirit  level  set  upon 
the  collars  on  which  the  collimators  turn.  This  is  effected  by  reading  the  level  when  the  col- 
limator is  in  its  regular  position,  and  when  reversed,  end  for  end,  around  a  vertical  axis,  the 
operation  being  repeated  a  number  of  times  in  succession  to  eliminate  the  possible  changes  of 
level  during  the  operation. 

The  following  are  the  level  indications  of  the  two  collimators  in  different  angles  of  position. 
The  angle  of  position  of  the  collimator  indicates  its  position  as  it  is  turned  upon  its  Ts,  with- 
out being  raised  from  them.  They  are  used  only  in  those  four  positions  in  which  one  of  the 
wires  is  horizontal;  and,  in  practice,  the  positions  are  almost  entirely  confined  to  two,  which 
are  designated  as  0°  and  180°.  The  angle  is  measured  by  the  position  of  the  clamp  which 
binds  the  eye-piece,  being  called  0°  when  this  clamp  points  horizontally  to  the  right  of  an  ob- 
server looking  into  the  eye  end  of  the  collimator,  and  90°  when  it  points  upward. 

The  collimator  is  said  to  be  direct  when  the  collimator  points  toward  the  Transit  Circle; 
reverse  when  it  points  from  it.  The  level  readings  are  positive  when  the  pivot  farthest  from 
the  Transit  Circle  is  too  high. 

COLLIMATOR  A. 

Ftr«<  acrtM.— Position  changed  from  0°  to  180°,  and  the  collimator  reversed  alternately 
one  pair  level  readings  between  each  change. 


PoeiUon  0°. 



FMltton  180°. 

Direct. 

Reverae. 

Diraet 

Reverse. 

Level  A   .     . 
Level  B    .     . 

d. 
f    3.84) 
+    8.91  J 
—    0.46 
-1-    0.08 

d. 
+    1.35 

—  0.78 

—  0.96 

d. 

+  ^fiX 

--    8.60$ 
■  -    l.OS 
-•    0.56 

d. 
+    1.86 

—  0.90 

—  1.08 

Meen.  D-R. 


+  1.32 


d. 
+  1.80. 


tk 


UNITBD  STATES  NAVAL  OBSERVATOBT. 


Second  »erie». — PoBition  0°. 


Third  amw.— Position  180°. 


Diraet. 
d. 
+0.81 

+0.32 

~0J84 

0.00 

Mean.  D~B. 

d. 
-0.18 
+0.36 
-0.39 


BareiM. 
d. 

-1.S4 

-0.94 

-1.42 

d. 
+1.42. 

d. 
-0.96 
-1.65 
-0.89 

d. 
+  1.09 


'-m  '•' 


Mean,  D— K. 

The  ooncloded  correction  for  diflFerence  of  collars,  when  in  the  position  0°  or  180®,  is  one- 
fonrth  D— E.  or  0".29,  the  eye-pivot  being  too  large. 

Two  similar,  but  more  accordant,  series  gave  for  the  correction  to  position  90°— 270° 
0".09,  so  that  the  collars  are  not  perfectly  cylindrical. 


OOLLIHATOB  B. 


The  results  are 


The  determinations  have  been  made  only  for  the  positions  0°  and  180°. 

d. 

D-B  for      0°,     +1.06  i         ;r^        . 

for  ISOO,     +0.66  ;  . 

Concluded  correction,  0".  17,  the  eye  collar  being  too  large,  as  in  the  other  collimator. 

The  collars  are  decidedly  conical,  diminishing  toward  the  ends  of  the  telescope,  so  that 
entire  dependance  cannot  be  placed  on  the  absolute  horizontal  point  obtained  from  a  single 
collimator.  But,  by  interchanging  the  collimators,  this  error  is  completely  eliminated  from  the 
zenith  point. 

(54)  Periodic  InequaliHeso^  i^he  Micrometer  Screws.— In  the  case  of  the  eight  microscope 
micrometers  the  inequalitie"  *«  --6  determined  by  measuring  the  intervals  between  the  parallel 
wires  of  each  pair  with  different  portions  of  the  screw.  The  circle  being  clamped  and  properly 
set,  one  of  the  micrometer  wires  was  brought  to  a  distance  from  the  edge  of  a  division  approx- 
imately equal  to  the  thickness  of  the  wire.  The  observer  retained  a  quite  accurate  idea  of  the 
intervening  space,  though  the  idea  could  not  be  defined  in  language.  The  micrometer  was 
then  read.  The  other  wire  was  then  brought  into  the  same  position,  and  the  micrometer  was 
again  read.  The  operation  was  twice  repeated,  making  three  measures  in  all.  The  circle  was 
then  moved  forward  6"  by  the  tangent  screw,  and  a  similar  series  of  measures  again  taken. 
The  operation  was  continued  through  the  two  revolutions  of  the  screw  most  used. 

Repeated  trials  showed  that  the  wires  could  be  set  more  accurately  in  position  by  this 
method  than  by  making  them  coincide  with  the  circle  division,  the  probable  error  of  a  single 
setting  being  about  0".10,  scarcely  greater  than  that  in  putting  the  division  midway  between 
the  wires. 

The  results  of  a  determination  made  in  November,  1865,  were: 

For  microacopes       I,  II,  III,  inequality  InsenBible ; 

IV.  Ineq.  =  — 0".63  cos  ti+0".67  sin  t»+0".13  cos  2i»— 0".l  1  ain  2« ; 

V.  —0  -0900811+0  .028ini(; 

VI.  +0  .24co8«+0  .aSsiDw; 

VII.  — 0  .06cos«+0  .06Bini»; 

VIII.  +0  .06coa«+0  JilBinu; 

u  being  the  angle  of  the  reading  of  the  head. 


n 


w^<i.„V>aw*|-jM— MWiWWWilll 


"mm 


w 


i; 


24 


OESOSIPTION   OF  THE   TRANSIT  OUtOLH   OF  THE 


WW 


;,i 


Microscopes  V-YIII  being  alone  employed  in  astronomical  operations,  their  inequalities 
were  redetermined  in  March,  1866,  with  the  following  result: 

V.  — 0".05  COB  «+0".05  sin  « ; 

VI.  +0  •84COBU+0  -Sfisinit; 

VII.  —0  .07cos«+0  .OSsiiiK; 

yill.  +0  .llcos«(+0  JS6tin«. 

The  mean  of  the  two  results  is  adopted  as  the  correction  for  the  year  1866. 

(55)  A  rough  check  upon  the  general  accuracy  of  the  screws  is  given  by  the  mean  dis* 
tance  of  the  wires  as  measured  in  different  revolutions  of  the  screw.  The  following  are  the 
distances  given  by  the  same  measures  which  determine  the  inequalities : 


'     1866. 

1666. 

Difference. 

29  nv. 

30  rev. 

29  rev. 

30  rev. 

1866. 

1866. 

Mic.       V     . 
Mic.      VI     . 
Mio.    VII     . 
Mic.  VIII     . 

10.98 
10.88 
10.63 
10.88 

// 

11.06 

10.82 
10.47 
10.87 

II 

10.80 
10.80 
11.86 
10.74 

// 

10.91 
10.95 
11.76 
10.92 

+    0.07 

—  0.06 

—  0.06 

—  0.01 

II 

+    0.11 
+    0.16 
-    0.10 
+    0.18 

The  method  of  observing  is  such  that  the  microscope  micrometers  are  seldom  moved  through 
more  than  a  fraction  of  a  revolution .  No  very  accurate  investigations  have  therefore  been 
made  to  find  whether  the  value  of  the  revolution  of  any  one  of  them  changes  progressively;  but 
the  measures  occasionally  made  for  runs  show  that  the  change,  if  it  exists,  is  entirely  inappre- 
ciable. 

There  are,  however,  outstanding  discrepancies,  amounting  sometimes  to  three  or  four 
tenths  of  n  second,  which  I  have  not  been  able  to  refer  to  any  law. 

(56)  The  Dedination  Micrometer  of  Telescope. — Neither  the  collimators  nor  the  telescope 
micrometer  were  originally  furnished  with  double  wires;  the  usual  method  could  not,  therefore, 
be  used  to  determine  the  inequality  of  the  lalter.  The  plan  was,  therefore,  adopted  of  meas- 
uring successive  half  revolutions  of  the  telescope  micrometer  with  the  microscope  micrometers, 
by  setting  the  wire  of  the  former  upon  the  collimator.  The  following  are  the  value  of  eight 
successive  half  revolutions,  as  given  by  two  microscopes  of  each  circle,  in  one  series,  and  the 
four  microscopes  V-VIII  in  the  other : 


Fint  Mriei. 

Mid. 

Mio.  III. 

Mic  VI. 

MicVm. 

Meui. 

r.         r. 

// 

// 

// 

// 

// 

24.0-24.6 

7.70 

7.61 

7.91 

8.39 

7.90 

24.5-85.0 

7.77 

7.76 

7.86 

7.49 

7.78 

85.0-85.6 

7.66 

7.37 

7.66 

7.66 

7.66 

85.5-86,0 

7.81 

7.41 

7.46 

7.41 

7.68 

86.0-86.5 

7.75 

7.86 

8.00 

&86 

7.96 

86.5  —  87.0 

7.86 

7.61 

7.63 

7.38 

7.60 

87.0  —  87.6 

7.65 

7.65 

8.03 

7.86 

7.77 

87.5  —  88.0 

7.83 

7.63 

7.61 

7.76 

7,71 

The  mean  of  the  odd  measures  is  7 ".80,  and  of  the  even  ones,  7".  64. 


•3  ■•V«r»WW««rfj*tTjn'^f«.:-*,'s^5»:tBBi 


UNITED  STATES  NAVAL  OBSEBVATOBY. 


Second  lerioi. 

MicL 

Mio.  III. 

Mlc.  VI. 

Mi«.VIII. 

Mean. 

r,           r. 

II 

// 

H 

// 

// 

31.25  —  31.75 

7.64 

7.fl9 

7.51 

7.36 

7.58 

31.75-38.85 

7.54 

7.9fi 

7.73 

8.02 

7.82 

38.25  —  32.75 

7.75 

7.66 

7.S6 

7.86 

7.78 

32.75-33.25 

7.51 

7.49 

7.24 

7.22 

7.36 

33. 2C- 33. 75 

7.37 

7.50 

7.64 

7.71 

7.56 

33.75  —  34.25 

7.57 

7.76 

7.6« 

7.61 

7.66 

34.25  —  34.75 

7.94 

7.64 

7.75 

7.85 

7.79 

34.75  —  35.25 

7.49 

7.57 

7.62 

7.60 

7.57 

J} 


\%  iM'-'%h'  '- 


The  meau  of  the  odd  lueasare  is  7".  66,  and  of  the  even  ones,  7".  60. 

From  the  differences  0".16  and  0".06  of  the  half  revolutions  the  screw  would  seem  to  be 

affected  with  the  error  . 

0".04co8«+0".02  8in«; 

an  error  so  Hmall  that  it  has  been  neglected,  especially  as  the  screw  is  used  about  equally 

through  several  revolutions  for  every  class  of  observations,  by  which  the  periodic  errors  will 

disappear  from  the  final  result  of  the  observations.     After  double  wires  were  placed  in  the 

collimators,  measurements  of  successive  half  revolutions  of  the  micrometer  were  made,  which 

gave  for  the  periodic  correction,  .  , 

0".07  COB  «— 0".05  sin  «. 

(57)  Value  of.  a  Revolution  of  the  Micrometer  /Screws.— 1866,  June  12. — The  telescope  was 
set  on  collimator  B.  The  record  does  not  state  whether  it  was  north  or  south.  The  microscopes, 
however,  indicate  that  it  was  south. 

The  following  readings  of  the  microscopes  and  zenith  distance  micrometer  were  taken 
successively  in  different  positions  of  the  telescope.  Each  micrometer  reading  is  the  mean  of 
nine;  three  for  coincidence  of  collimator  image  with  each  wire,  and  three  for  a  position  midway 
between  wires: 


I 


•■ 


' 


JS 

.a 

1 

1^ 

Readings  of  microecopes— 

Corr.  for— 

"^* 

•s-^ 

Mean. 

!^ 

*\ 

1^ 

^i 

1 

1 

V. 

VI. 

vn. 

vra. 

lueq. 

Div. 

c 

5 

( 

r.     " 

// 

// 

41 

II 

/     It 

r. 

56 

9  19.5 

SO.  3 

21.2 

23.7 

21.18 

-  .16 

-  .04 

56  50.99 

28.408 

.54 

16.5 

18.0 

19.2 

21.8 

18.89 

-  .14 

—  .12 

53  48.63 

20.392 

58 

21.4 

22.8 

23.2 

26.0 

23.35 

~  .12 

+  .16 

57  53.39 

.%.377 

64 

15.8 

17.9 

18.9 

21.2 

18.45 

-  .14 

—  .12 

53  48. 19 

20.373 

58 

21.6 

22.8 

23.4 

25.9 

23.43 

-  .12 

+  .16 

57  53.47 

36.393 

66 

19.0 

20.6 

21.4 

23.7 

21.18 

-  .15 

-.04 

65  60.99 

28.395 

These  readings  give  from  20  r.  to  28  r.,     1  rev.  =15".286, 

28  r.  to  36  r.,     1  rev.  =15  .337. 
An  increase  in  the  value  of  a  revolution  as  the  turns  increase  seems  to  be  indicated. 

In  the  great  majority  of  observations  the  micrometer  is  used  between  26  and  34  revo- 
lution?;  a  determination  of  the  value  between  those  limits  was  therefore  made  which  gave 
I5".296.     The  value  actually  adopted  was  the  mean  of  the  two  determinations,  or  15".303. 

A  third  determination,  made  on  September  3,  1866,  gave 

From  26  r.  to  34  r.,     1  rev.  =il5".311 ; 
34  r.  to  4fi  r.,     1  rev.  sl5  .375 ; 
which  seems  to  confirm  the  suspicion  of  an  increase  in  the  value  of  a  revolution  as  the  screw 

is  advanced. 

4 


'^^*h~^--m&^St 


MPtWM 


mmKmieMms&satmmmmsi/^mwtmim^xm^ 


hi 
li 


26 


DESCBirnOH  OP  THS  TRAKSrr  OIBOLS  OP  THE 


^: 


(58)  Irregularity  of  the  Screw. — It  is  desirable  to  know  whether  this  change  in  the  valae 
of  revolution  is  regularly  progressive,  or  whether  it  is  subject  tr  sudden  changes.  To  learn 
this,  advantage  was  taken  of  the  fact  that  the  distance  of  the  pair  of  wires  in  collimator  A, 
and  of  the  close  pair  of  wires  moved  by  the  micrometer,  are  together  nearly  equal  to  a  revo- 
lution of  the  latter.  Consequently,  turning  the  telescope  on  that  collimator  when  its  double 
wires  are  horizontal,  we  have  a  measure  of  a  constant  space  by  setting  first  the  upper  microme- 
ter wire  on  the  lower  image  of  the  collimator  wire,  and  then  the  lower  micrometer  wire  on  the 
upper  image.  The  measures  were  commenced,  as  nearly  as  practicable,  at  an  even  revolution, 
and  therefore  ended  nearly  at  the  beginning  of  the  next  revolution.  The  measures  were  made 
on  three  different  dates,  and  three  measures  of  each  revolution  made  on  each  date.  But  the 
measures  were  not  always  continued  through  the  entire  range  of  the  screw.  About  30  revolu- 
tions they  were  prevented  by  the  interference  of  the  fixed  horizontal  wires  of  the  reticule. 


a  1 

I 

IfeaniN. 

1 

i 

^ 

h 

1 

Her. 

Arc. 

Cor.  arc 

1 

r. 

r. 

r. 

// 

II 

// 

17.7 

18.7 

0.964 

15.06 

14.97 

+    0.13 
--    0.18 

1 

18.7 

19.7 

.964 

15.06 

14.97 

1 

19.6 

20.6 

.978 

14.88 

14.80 

—    0.05 

1 

30.0 

21.0 

.986 

15.09 

15.03 

-f    0.17 
+    0.08 

3 

80.5 

21.5 

.980 

15.00 

14.93 

4 

81. 0 

88.0 

.971 

14.86 

14.79 

—    0.06 

4 

28.0 

83.0 

.976 

14.94 

14.88 

-1-    0.03 

4 

33.0 

84.0 

.978 

14.88 

14.63 

—    0.02 

3 

84.0 

85.0 

.973 

14.89 

14.85 

0.00 

3 

85.0 

86.0 

.966 

14.77 

14.73 

—    0.13 

3 

86.0 

27.0 

.973 

14.88 

14.85 

0.00 

3 

27.0 

88.0 

.965 

14.77 

14.75 

—    0.10 

3 

88.0 

80.0 

.964 

14.76 

14.75 

—    0.10 

3 

31.0 

33.0 

.970 

14.85 

14.86 

-1-    0.01 

3 

38.0 

33.0 

.968 

14.88 

14.83 

—    0.08 

3 

33.0 

34.0 

.976 

14.93 

14.94 

-)-    0.09 

1 

34.0 

35.0 

.961 

14.71 

14.74 

-    0.11 

1 

35.0 

36.0 

.965 

14  77 

14.81 

—    0.04 

I 

36.0 

37.0 

.966 

14.79 

14.83 

-    0.08 

1 

Of  the  three  columns  headed  "Measure,"  the  first  gives  the  measures  in  revolutions  of  a 
micrometer;  in  the  second  these  revolutions  are  turned  into  arc,  using  1  rev.ssl6".303 ;  in 
the  third  they  are  corrected  for  progressive  change  in  the  value  of  the  revolution.  The  resid- 
uals show  the  excesses  of  the  individual  corrected  measures  over  the  mean  value  14".  85.  I 
conceive  that  they  proceed  mainly  from  the  accidental  errors  of  reading  and  temporary  derange- 
ments of  the  motion  of  the  screw  by  dust,  displacement  of  the  oil,  and  other  causes,  and  that 
the  screw  itself  may  be  regarded  as  sensibly  regular. 

'  (59)  J7.  A.  Micrometer. — ^The  value  of  a  revolution  of  this  micrometer  seems  to  be  exactly 
the  same  as  that  of  the  other.  Wide  measures  give  15".  300.  Owing  to  its  limited  use,  no 
special  investigation  of  its  movement  has  been  entered  upon. 

(60)  Flexure  of  the  Cirdes.—The  work  of  determining  separately  the  flexure  of  the  different 
parts  of  each  circle  was  commenced  in  1866,  January  19.  But  after  taking  one  series  of  read- 
ings, it  was  found  that  the  axes  of  several  of  the  microscopes  deviated  quite  sensibly  from  the 
perpendicular  to  the  face  of  the  circle;  some  deviating  as  much  as  40'.  To  adjust  them  with 
entire  accuracy  appeared  to  be  a  difficult  and  troublesome  operation ;  but  a  kind  of ^  T-square 
was  made  by  which  they  could  be  set  without  an  error  exceeding  5',  and  they  w^re  adjusted 
by  it  on  April  7.     The  set  of  readings  previously  made  were  not  used. 

The  following  are  the  details  of  the  operations  by  which  the  definitive  values  of  the  flexure 
coefficients  were  obtained: 


UNITBD  STATU  VAVAL  OBSKBYATOSY. 


%1 


In  the  first  series  of  readings  the  position  of  the  circles  wm  snch  that  when  the  telescope 
pointed  to  the  senith,  the  divisions  of  circle  A,  which  were  nnder  microscopes  V-VIII,  were: 

MIc.  V,  ISfiO;    VI,  2SfiO;    VII,  31 5°  j    VIII,  IfiO 
The  divisions  of  circle  B,  under  microscopes  I-IV,  were: 

Mie.1,  3160.    II,  4AO;    III,  ISfiO.     IV,  SSfiO. 

When  the  telescope  pointed  at  senith  distance  s,  the  above  readings  of  microscopes  V-VIII 
wonld  be  increased,  and  those  of  I-IV  diminished  by  i. 

The  operation  was  began  on  divisions  0°,  90<^,  180°,  270°.  The  division  0°  of  circle  B  was 
brought  under  microscope  I,  and  the  eight  microscopes  were  read ,  one  observer  reading  each 
circle.  The  telescope  was  then  turned  90°,  and  the  microscopes  were  again  read.  The  tele- 
scope was  again  turned  90°,  and  the  operation  of  turning  and  reading  continued  until  the 
microscopes  had  been  read  three  times  in  each  6(  the  four  positions  of  the  telescope.  The 
mean  of  the  three  readings  was  taken  as  that  corresponding  to  each  position. 

The  telescope  was  then  set  15°  backward  from  its  first  position,  and  the  same  operation 
was  performed  on  divisions  75°,  165°,  Ac,  of  circle  A,  and  15°,  105°,  Ac,  of  circle  B.  The 
operation  was  repeated  through  every  15°  of  the  quadrant.    The  first  series  was  now  complete. 

In  the  second  series  circle  A  was  loosened  and  turned  180°  on  its  axis,  so  that  when  the 
telescope  pointed  to  the  senith,  the  division  315°  was  under  microscope  V.  A  series  of  read- 
ings  exactly  like  the  first  was  then  made  on  the  two  circles. 

Circle  B  was  then  turned  on  its  axis  180°,  and  a  third  series  of  readings  were  made. 

Finally,  circle  A  was  returned  to  its  original  position,  and  a  fourtb  series  of  readings  were 
made. 

The  mean  of  the  three  readings  for  each  position  of  the  instrument  is  given  in  the  foUoW' 
ing  table: 

8EBIES  I. 


I 

I 


I 


46 

las 

986 
315 

30 
190 
310 
300 

15 
106 
196 
986 

0 

90 

160 

£70 

346 

75 

165 

966 

330 

60 

160 

940 


9.0 

180 

00 

0 

986 

106 

106 

16 

300 

910 

190 

30 

316 

996 

136 

45 

330 

940 

160 

60 

345 

965 

165 

78 


180 

970 

0 

00 

166 

966 

346 

76 

160 

940 

330 

60 

136 

996 

315 

45 

190 

910 

300 

30 

106 

105 

985 

15 


Beading*  of  micnwcopM. 


97.00 
97.40 
93.43 
94.37 

96.57 
96.43 
93.47 
99.97 

96.87 
97.3:1 
94.03 
93.17 

96.57 
97.73 
96.47 
93.30 

96.03 
97.13 
96.37 
99.86 

94.77 
97.43 
96.30 
99.70 


n. 


95.63 
95.60 
93.70 
91.00 

33.67 
95.10 
93.70 
90.13 

84.77 
95.03 
93.63 
91.50 

93.00 
96.00 
94.60 
99.35 

99.43 

96.07 
94.17 
99.60 

91.97 
96.87 
95.57 
99.37 


m. 


4.97 
4.77 
3.73 
3.07 

3.40 
3.83 
4.40 
1.80 

4.67 
4.77 
3.30 
9.47 

4.53 
5.33 
4.70 
9.60 

3.30 
4.70 
4.03 
9.60 

3.10 
4.60 
4.93 
3.13 


lY. 


0.67 
99.13 
97.83 
98.50 

98.03 
98.87 
97.00 
87.17 

99.70 
90.40 
97.07 
97.03 

90.97 

0.40 

97.77 

97.75 

98.13 

0.93 

87.47 

97.36 

98.57 

0.03 

88.67 

97.57 


V. 


4.07 
5.33 
5.43 
4.50 

6.93 
6.30 
5.80 
6.10 

4.83 
5.97 
6.00 
6.17 

4.67 
4.67 
4.93 
5.00 

5.83 
6.17 
5.33 
5.45 

5.80 
5.97 
5.40 
6.33 


VI. 


7.07 
6.87 
4.63 
6.73 

8.60 
8.00 
4.47 
8.60 

6.83 
7.43 
5.60 
6.77 

7.30 
6.67 
6.07 
6.90 

8.13 
7.00 
6.43 
5.35 

7.70 
7.77 
6.30 
6.77 


YU. 


8.87 
0.67 
8.17 
4.57 

4.77 
1.83 
1.63 
5.57 

3.67 
1.67 
1.43 
4.63 

a03 
1.50 
0.63 
6.80 

4.17 
8.87 
1.03 
8.96 

5.03 
3.30 
0.93 
9.83 


Yni. 


3.43 
a  10 
3.80 
5.63 

4.13 
9.37 
3.97 
5.16 

6.60 
9.93 
3.73 
4.80 


■MwiwilMlM 


mumm 


M 


'#' 


315 

45 

136 

886 

300 

30 

190 

SIO 

985 

15 

106 

196 

870 

0 

90 

180 

856 

346 

75 

166 

840 

330 

<M) 

150 


DESCRIPTIOir  or  THE  TKANSIT  OIBOLK  OW  THK 
8EKIEB  II. 


o 
0 
870 
IHO 

90 

16 
886 
196 
106 

30 
300 
310 
180 

45 
315 
885 
136 

60 
330 
840 
150 

75 
345 
856 
165 


195 

885 

15 

105 


Raitdingf  of  microMsopM. 


89.00 

1.70 

86.90 

85.36 

86.70 

0.80 

87.40 

84.73 

84.80 
98.97 
96.70 
89.80 

83.67 
87.77 
86.47 
83.30 

89.73 
86.90 
87.03 
83.80 

89.50 
86.80 
87.47 
84.87 


II. 


88.30 

0.90 

96.65 

96.35 

96.00 
99.93 
97.63 
96.57 

94.93 
87.90 
96.17 
83.37 

83.77 
85.90 
96.73 
83.33 

83.60 
95.13 
97.10 
99.97 

83.10 
96.37 
97.13 
94.10 


III. 


6.70 
7.30 
9.96 
3.45 

4.60 
6.87 
3.00 
a90 

9.33 
4.67 
8.17 
0.67 

0.66 
.^57 
9.07 
0.63 

0.83 
3.13 
9.97 
0.10 

0.80 
3.99 
3.47 
0.77 


IV. 


0.45 

1.50 

96.56 

96.86 

98.73 

0.80 

86.30 

84.77 

86.63 
88.53 
95.63 
89.83 

84.57 
87.03 
86.97 
88.73 

83.83 
96.77 
87.30 
89.40 

83.93 
87.80 
97.33 
93.93 


4.70 
5.10 
6.06 
6.80 

6.67 
5.73 
6.37 
6.40 

6.17 
6.33 
6.57 
6.57 

7.17 
7.33 
7.90 
7.13 

7.00 
7.10 
6.87 
7.00 

7.  S3 

7.07 
6.97 
7.97 


VI. 


VII. 


8.40 
5.80 
8.36 
9.66 

9.90 
6.80 
7.60 
9.97 

11.10 
7.63 
7.00 
9.77 

11.93 
9.33 
8.97 

10.53 

10.80 

10.47 

7.90 

10.93 

11.70 

10.43 

7.87 

9.83 


0.40 

98.76 

3.80 

4.60 

1.83 

99.67 

9.77 

4.53 

a60 
0.10 
9.60 
6.67 

4.70 
1.47 
9.77 
6.80 

5.60 
1.83 
1.60 
6.37 

6.03 
9.37 
1.33 
5.90 


SERIES  m. 


VIU. 


90.70 

30.30 

4.66 

9.56 

1.50 
0.87 
4.93 
9.37 

9.13 
0.77 
4.43 
4.90 

9.67 
9.07 
4.07 
6.07 

3.00 
9.03 
9.90 
6.70 

3.98 
1.93 
3.07 
5.83 


135 

0 

90 

96.30 

94.80 

6.40 

97.97 

6.57 

9.40 

4.47 

4.93 

885 

870 

180 

89.57 

97.80 

6.77 

98.93 

8.77 

10.37 

6.17 

3.50 

315 

180 

870 

88,77 

98.63 

6.87 

96.50 

6.90 

10.87 

3.37 

9.90 

45 

90 

0 

86.17 

97.80 

7.17 

96.63 

7.80 

ao3 

1.97 

a90 

ISO 

15 

76 

83.70 

93.17 

4.97 

96.40 

7.37 

0.07 

4.87 

6.77 

810 

985 

166 

98.40 

85.87 

4.30 

97.70 

7.17 

10.60 

6.73 

3.93 

300 

196 

956 

98.07 

93.03 

4.40 

96.90 

7.10 

11.47 

3.70 

9.97 

30 

106 

345 

96.53 

97.87 

6.97 

94.93 

7.00 

7.47 

1.93 

9.33 

106 

30 

60 

94.93 

84.40 

6.47 

96.10 

6.70 

8.37 

3.10 

4.63 

196 

300 

150 

87.60 

94.97 

4.47 

97.97 

6.83 

0.97 

6.67 

4.97 

986 

910 

940 

98.40 

97.30 

4.40 

96.70 

e.'v 

11.67 

4.17 

9.87 

16 

180 

330 

96.17 

97.03 

6.17 

94.80 

6.93 

8.97 

OOS 

1.60 

90 

46 

45 

93.63 

84.80 

6.97 

96.00 

7.63 

8.07 

8.93 

4.60 

180 

315 

135 

96.67 

83.07 

4.63 

96.47 

7.37 

10.87 

6.77 

6.13 

970 

886 

985 

87.63 

96.70 

3.60 

96.87 

7.67 

19.40 

6.90 

3.47 

0 

136 

315 

96.80 

96.87 

6.00 

94.17 

7.70 

9.00 

1.80 

9.63 

78 

60 

30 

93.90 

86.83 

6.00 

95.80 

7.37 

7.40 

1.90 

8.43 

166 

330 

180 

96.80 

93.97 

6.77 

96.93 

7.80 

10.40 

6.30 

6.70 

966 

940 

810 

87.87 

96.97 

3.00 

96.97 

7.30 

11.30 

5.60 

a30 

345 

160 

300 

96.77 

96.M 

6.70 

84.90 

7.93 

10.07 

9.10 

9.40 

60 

76 

15 

94.37 

96.70 

6.90 

96.00 

7.93 

7.n 

1.47 

3.«7 

160 

346 

105 

96.77 

93.80 

6.63 

97.30 

7.98 

9.67 

5.13 

6.87 

840 

966 

195 

98.17 

96.60 

4.63 

97.30 

7.13 

11.40 

6.77 

4.03 

330 

166 

886 

97.50 

98.00 

6.90 

86.97 

7.93 

10.63 

9.63 

9.13 

BM 


uirmD  iTATn  watal  OBtnnrAToxr. 


8EHIE8  IT. 


1.' 

li 

if 

Baadiofft  of  tlM 

niiofOfloopM. 

I. 

II. 

m. 

IV. 

V. 

VI. 

VII. 

vm. 

o 

0 

o 

// 

II 

II 

II 

// 

II 

// 

«» 

316 
46 

0 

870 

ISO 

00 

870 

0 

00 

180 

88.87 
96.33 
93.90 
19.40 

90.97 
93.63 
99.33 
91.67 

3.60 

8.47 

90.87 

1.73 

95.60 
96.17 
90.77 
90.17 

5.90 
5.87 
5.67 
6.37 

8.80 
6.43 
7.97 
8.80 

1.10 

99.93 

3.33 

3.63 

0.33 
1.87 
4.73 
a  17 

190 

no 

300 
30 

16 
966 
106 
106 

956 

346 

75 

166 

91.07 
97.10 
83.80 
90.33 

90.90 
93.53 
93.13 
98.37 

3.47 
3.17 
0.17 
1.93 

96.03 
96.77 
91.93 
19.70 

6.13 
5.13 
6.07 
5.90 

8.80 
5.33 
7.00 
8.00 

1.90 

90.90 

9.17 

3.10 

1.70 
0.73 
a  03 
8.07 

106 

106 

9H6 

16 

30 

30O 
910 
190 

940 

330 

60 

150 

90.70 
96.80 
94.47 
90.47 

80.33 
83.10 
88.93 
88.10 

9.40 
9.83 
0.93 
1.30 

93.07 
96.80 
91.93 
19.93 

6.13 
6.17 
5.90 
5.93 

0.37 
6.13 
6.70 
7.37 

9.93 

90.33 

1.13 

a  10 

•8.00 
0.80 

a  80 

8.80 

00 

180 

870 

0 

46 
316 
985 
136 

986 

315 

45 

136 

90.43 
86.40 
84.70 
90.63 

81.47 
88.50 
83.33 
81.80 

1.97 
3.60 
0.60 
0,37 

99.83 
96.80 
93.93 
18.60 

6.17 
6.30 
6.07 
5.33 

8.83 
6.57 
6.60 
8.90 

9.17 

99.47 

0.83 

a33 

1.53 
0.67 
9.57 
a  43 

76 
166 
986 
346 

60 
330 
940 
160 

910 

300 

30 

190 

19.07 
93.97 
95.13 
91.47 

81.30 
81.00 
8a  63 
81.37 

1.70 
9.80 
1.40 
0.10 

91.63 
94.97 
94.73 
18.47 

5.90 
5.30 
6.97 
5.13 

8.93 
8.03 
5.  .17 

7.83 

9.73 

0.07 

89.90 

8.63 

1.80 
1.03 
1.47 
a  90 

60 
150 
940 
330 

76 
346 
956 

166 

195 

386 

16 

106 

10.30 
83.60 
85.77 
89.90 

81.10 
81.43 
83.63 
88.17 

1.07 
9.03 
1.67 
0.17 

90.00 
96.60 
94.03 
19.77 

6.63 
6.70 
5.60 
5.47 

9.17 
8.53 
6.83 
7.80 

a  67 
0.83 
0.10 
a  87 

9.73 

0.97 
9.07 
4.90 

One  of  the  most  obvioua  couclasioiis,  from  the  above  table,  is  that  the  two  ciroleo  do  not 
give  the  same  result  for  the  distance  the  telescope  has  moved.  If  they  did,  the  sum  of  the 
eight  microscope  readings  would  be  constant  for  each  series  and  each  set  of  circle  divisions. 
In  the  first  set  of  the  first  series,  for  instance,  there  is  a  difierence  of  1".45  after  the  circle  has 
been  turned  180°.     One  or  both  circles  are  therefore  affected  with  a  quite  sensible  flexure. 

The  above  readings  were  corrected  for  inequality  of  screw,  and  the  flexare  coefiicients 
were  then  computed  from  the  formula)  already  given.  We  give  an  example  of  the  form  of 
computation  adopted,  by  presenting  in  full  so  much  of  the  computation  as  relates  to  the  four 
cardinal  divisions. 

8EBIES  I. 


■» 


Zo=3160;  a=90o  o'=0° 

z 

9K.15 

9K.I6 

9K.96 

8K96 

8a.« 

8/?.« 

e^.zo 

ap.i 

^9 

9p.b 

9pA 

Ml+S) 

s^d-HJ) 

»>>.(9+5) 

S^-(9+«) 

o 

II 

II 

II 

II 

II 

II 

// 

II 

II 

II 

II 

II 

II 

// 

// 

316 

98.0 

19.9 

9.1 

19.7 

7.1 

10.7 

99.0 

9.6 

-1.0 

—1.7 

-1.9 

-1.0 

-8.7 

^8.3 

+    0.8 

46 

39.9 

96.0 

7.8 

10.5 

10.7 

ia4 

33.8 

6.5 

+5.9 

+5.0 

+5.9 

+5.9 

—8.3 

—1.7 

-    0.5 

136 

39.9 

94.3 

5.9 

10.9 

8.1 

13.4 

30.3 

4.5 

^         ^ 

. 

. 

^          ^ 

-1.9 

—1.4 

+    0.4 

895 

87.9 

90.3 

7.6 

10.3 

4.8 

7.5 

97.9 

0.6 

•     • 

•     • 

•     • 

—9.1 

-1.9 

-    0.3 

SERIES  n. 

o 

9K'.16,«te. 

%a.h 

-S-5 

// 

315 

36.3 

98.4 

5.0 

8.4 

11.3 

14.7 

a4 

6.8 

ti;; 

+1.5 

+a7 

+1.1 

KS 

--1.3 

0.0 

46 

39.0 

39.1 

4.8 

6.0 

ia8 

16.0 

6.9 

8.1 

+6.1 

-^.8 

—8.8 

--    0.9 

135 

99.8 

88.5 

9.8 

ia4 

9.6 

ta8 

9.3 

6.9 

. 

,         ^ 

-1.7 

-0.8 

..    0.6 
+    1.5 

986 

98.8 

91.4 

10.4 

18.5 

9.9 

11.3 

1.8 

a9 

-     • 

•   • 

-     • 

-     - 

+8.9 

—1.0 

'-.%^- 


:.y^gifM^ppm-pt-,-!S-a6=;»,-;it-«Jf-n    ■ .  WMi«W!«.u»ilWMi««I»l«»iB* 


ti 


SO 


DiaOBIPTIOIf  OP  THK  TRAMfllT  OBOLK  OF  THE 
SERIEfl  ni. 


z 

Z,r=316°;  «»:90O  M'saOO 

9K".16.«to. 

Sa'ui 

8^.« 

vg\gtvrw)\ 

%>.! 

8^.8 

8p.5 

%>.6 

a>,.(l+6)a>..(l+6)9^.(8+6)|9^.(8+6) 

o 

II 

// 

// 

t/ 

// 

II 

// 

II 

II 

II 

II 

II 

II 

II 

// 

315 

4.6 

84.5 

10.3 

14.0 

14.9 

18.6 

4.8 

8.5 

+1.8 

+1.8 

+1.6 

+1.6 

-0.3 

+10.8 
+10.1 

0.0 

45 

8.3 

99.7 

9.1 

11.7 

11.4 

14.0 

1.6 

4.4 

-6.9 

—5.6 

—6.6 

-6.1 

—8.1 

+ 

0.4 

135 

8.7 

98.9 

11.0 

14.7 

13.7 

17.4 

3.8 

6.9 

•          • 

^          , 

^          , 

+0.5 
+0.3 

+11.6 
+10.3 

0.6 

896 

6.3 

96.3 

19.0 

14.9 

17.3 

19.6 

6.3 

10.5 

•     • 

•     • 

•     • 

•     • 

— 

0.8 

HERIE8  IV. 

0 

8a'.» 

9fif.h 

315 

83.1 

19.6 

0.0 

13.8 

38.1 

6.3 

81.6 

96.8 

-0.7 

+0.4 

—0.6 

+0.6 

-10.1 

-0.7 

— 

0.6 

45 

9t.l 

11. a 

*  9.9 

18.4 

30.3 

3.5 

80.5 

83.7 

-4.8 

-4.1 

—4.3 

-4.8 

—10.0 

-9.6 

— 

1.4 

135 

86.5 

15.8 

6.3 

0.4 

39.8 

6.9 

89.1 

85.8 

•          • 

•          • 

^          ^ 

^         _ 

—10.5 

—0.5 

+ 

0.8 

885 

88.8 

19.1 

6.7 

6.8 

34.5 

7.6 

94.8 

87.9 

•     • 

•          • 

•     • 

•     • 

—  9.8-0.7 

0.0 

The  oompntation  for  the  other  divisions  was  performed  iu  the  same  way.  The  complete 
results  for  every  15°  are  given  in  the  following  table,  which  is  so  arranged  that  the  two  coeffi* 
cients  which  correspond  to  the  same  pqsition  of  the  circle  are  under  each  other.  For  this 
purpose  some  of  the  angles  are  changed  by  180°,  and  the  signs  of  the  coefficients  are  changed 
to  correspond. 

CIBCLE  A. 


«=s 

OO 

16° 

30° 

45° 

600 

76° 

90O 

106O 

190" 

1360 

160° 

1660 

VkluMofSa^i 

II 

—1.3 
-0.8 
—1.7 
-41.8 

-0.19 

II 
—4.0 
—3.9 
—3.1 
-A8 

—0.41 

-3.8 
—3.3 
-8.4 
-8.6 

-0.38 

-0.9 
—0.8 
-9.9 
—3.1 

-0.84 

// 

-9.4 
—8.5 
—3.8 
—3.3 

—0.38 

II 

-9.7 
-«.8 
-9.6 
-9.7 

—0.34 

II 

—9.7 
-8.3 
—1.9 
-8.1 

— o.8e 

II 
—0.7 
—9.1 
—1.6 
—9.1 

—0.90 

II 

-1.8 

0.0 

—0.6 

—1.4 

-0.10 

1/ 

-1.9 
—0.9 

-0.01 

II 

+0.9 
+0.6 
+1.3 
+0.8 

+0.11 

II 

+1.6 
+0.8 
-.0.9 
+1.7 

+0.16 

— 

90O 

106O 

180° 

136° 

160O 

1660 

180O 

1950 

910O 

9800 

940O 

966° 

f 

YalnnofS^.* 

// 
-9.9 

—1.9 
—0.89 

II 

-3.1 
^2.3 
—3.0 
—9.7 

-0.35 

II 

-3.1 
—8.6 
—8.9 
-3.1 

-0.37 

// 

-8.6 
—8.6 

-8.8 
-8.9 

— 0.3« 

II 

-3.3 
—8.4 

— 4.  i 
—8.6 

— 0.«li 

// 
».'3.0 

— ».e 

™3.f' 
— •./.38 

It 

-3.9 
-9.8 
-0.8 
—1.0 

-0.84 

II 

—0.8 
—1.9 
—1.1 
—1.7 

—0.16 

—0.7 

+0.5 

0.0 

-0.9 

-0.03 

II           II 

+0.8     +0.6 
+1.8     +0.9 
-0.6     +1-3 
—0.3     -^.8 

+0.03  +0.09 

II 
+9.0 
+1.3 
+0.6 
+1.4 

+0.17 

CIBCLE  B. 


•^ 

0° 

le'' 

30° 

4^ 

60O 

760 

90° 

106O 

190" 

1360 

160O 

1860 

II 

II 

II 

// 

II 

II 

II 

II 

II 

II 

II 

II 

Valne«of8«'.« J 

-0.3 
—8.1 
+0.6 
+0.3 

-9.8 
-9.8 
—9.1 
—9.1 

-4.1 

-4.8 
—5.8 
-6.6 

—4.7 
-6.7 
-6.7 
-0.9 

—8.4 
-8.0 
—7.0 
—7.8 

-0.1 

-8.8 
-8.9 
-8.7 

-10.1 
—10.0 
-10.5 
—  9.9 

—9.7 
-0.9 
-9.1 

—8.6 

—8.9 
—7.9 
-8.6 
-8.6 

-8.9 
—7.7 
-6.8 
-6.3 

-4.8 
-.4.8 
-f6.& 
-6.5 

-8.6 
—1.8 
—1.7 
-1.9 

a'.«=r 

—0.06 

—0.97 

-^.63 

-0.77 

-0  98 

-1.09 

-1.84 

—1.16 

—1.04 

-0.89 

-0.64 

-0.99 

UmraD  ITATBS  MATAL  0B8BBTAT0BT. 


n 


OIBOLE  B.— OonMniMd. 


■  SB 

90° 

106O 

180° 

135° 

1600 

166° 

160O 

I960 

810° 

886° 

840» 

885'> 

ViivmolS^.* 

II           II 

-0.7     -1.9 
-8.6     -1.9 
-0.6     —1.8 
—0.7     —1.8 

-0.14  ~«.83 

./            II 

-4.8     -4.1 
—4.9     -6.1 
-6.0     -6.4 
-&.1     -6.6 

-0.60  -0.79 

II 

-8.8 
—8.4 

-ai 

-8.9 
—1.07 

// 

-9.3 
-9.0 
-S.9 
-9.4 

—1.14 

II            II 

-10.9  -  9.6 
-10.1    -  9.7 
—11.6  —10.4 
-10.3  —  9.8 

-  1.38—  1.83 

II 

-8.4 
-8.1 
-8.7 
-«.7 

—1.06 

II            II 

-«.0     —5.1 
—7.5     -5.1 
-6.0     —3.8 
-6.0     —3.7 

—0.86  —0.66 

-8.7 
-8.0 
-8.7 
-9.8 

-0.30 

(61)  It  will  be  remembered  that  a  represents  the  excess  of  reading  of  microsoopea  Y-YII, 
when  a  division  of  circle  A  is  brought  under  microscope  Y,  and  ^  the  excess  of  YI-YIII,  when 
a  division  is  brought  under  microscope  YI.  Also,  when  the  division  a  is  under  mioroncope  Y, 
the  division  a-f90°  is  under  microscope  YI.  The  same  remarks  hold  true  for  circle  B,  by 
diminishing  the  number  of  the  microscope  hy  lY.  Now,  comparing  the  values  of  a  with  those 
of  p  immediately  under  them,  it  will  be  seen  that  there  is  generally  a  quite  dose  agreement, 
the  difference  amounting  to  one*tenth  of  a  second  in  only  one  case  out  of  the  tw«nty-four,  and 
the  mean  difference  being  less  than  0".05.  If  we  suppose,  as  seems  probable,  that  these  differ* 
ences  are  no  greater  than  the  unavoidable  errors  of  the  determinations,  we  arrive  at  tbe  con- 
clusion : 

Hie  geometriced  form  of  the  oirde  rdalive  to  any  ayatem  of  Jhced  aae»  rem^ii'\n  invariable  a» 
U  revolve$. 

The  large  values  of  a  and  fi  show  that  if  the  central  part  of  the  cirde  revoi  untforndy,  the 
drcutnftrmoe  don  not  revolve  tm^ormly,  ha  is  qfected  with  a  periodic  inequality 

I  am  disposed  to  attribute  this  singular  phenomena  to  a  slight  deviation  of  the  centre  of 
gravity  of  the  circle  from  its  centre  of  figure.  The  circles  weigh  about  80  pounds  each,  and 
a  weight  of  a  few  ounces  on  their  circumference  is  sufficient  to  produce  a  flexure  of  1".  But 
to  whatever  cause  we  attribute  it,  the  circumstance  of  invariability  of  form  of  the  circle  involves 
the  law  that  the  flexure  shall  be  of  the  form  of  a  sin  x+b  cos  s.     If,  then,  we  suppose 

a  a  A  sin  (D  +460)+B  cos  (D  +  4fiO). 
/9  sA  sin  (D -460)+B  COS  (D -450),' 
o'sbA' sin  (D'-f  460)+B' cos  (D'+460), 
/ysA' sin  (iy-460)+B' cos  (D'-4fiO). 

D  being  the  circle  division,  we  flnd  by  equating  the  preceding  values  of  a  and  ^,  and  solving 

by  least  squares, 

A=-0".37;  B«i+0".01} 

A'—0".84;  B'=!+0".86. 

(62)  The  outstanding  apparent  errors  are  seen  in  the  following  table,  which  includes  the 
combined  errors  of  the  two  hypothesis;  first,  that  the  geometrical  form  of  the  circle  remains 
invariable,  in  other  words,  that 

«ua=/J.(a+90O). 

Second,  that  a  and  0  are  each  of  the  form, 

AsinD+BeosD. 

The  first  column  of  the  table  gives  the  reading  of  the  finding  microscope,  which,  for  circle 
A,  is  midway  between  Y  and  YI,  and  for  circle  B,  midway  between  I  and  II. 

The  second  gives  the  flexure  for  that  position  of  the  circle  as  computed  by  the  formnle, 
which  is  assumed  to  be  the  same  for  each  pair  of  microscopes. 


^jiEjsS«i»saM».;i5s%5!S: 


I 


h 


t  fl- 


am- DESCBIPTION  OF  THE  TRANSIT  CIBCLE  OF  THE 

The  third  gives  the  observed  flexnre  of  the  mean  of  microscopes  VI- VII,  or  I-III,  for  that 
position  of  the  circle,  in  other  words,  the  value  of  a.(R— 45°.) 

The  fourth  gives  the  observed  flexure  of  the  mean  of  microscopes  VI-VIII,  or  II-IV,  for 
the  same  position  of  the  circle,  or  the  value  of  ^.(R+45°.) 

The  lifth  and  sixth  give  the  outstanding  errors. 


R 

Flexure 
formula. 

ObBorved  flexure. 

Errors, 

R' 

Flexure 

by 
formula. 

Obserred  flexure. 

£rron. 

V-VII. 

VI-VIII. 

V-VII, 

VI-VIII. 

i-m. 

II-IV, 

i-in. 

II-IV. 

o 

46 

60 

75 

90 

105 

120 

135 

150 

165 

180 

195 

210 

225 

// 

—0.25 
—0.31 
-0.36 
-0.37 

— o.:}6 

—0,32 
-0,27 
—0,19 
-0,11 
—0.01 
4-0. 09 
+0,18 
+0.25 

// 

—0.19 
—0.41 
—0,38 
—0,24 

— o.:« 

—0,34 
—0.28 
—0.20 
—0.10 
—0,01 
+0.11 
+0.  15 
+0.16 

// 

—0.22 
—0.35 
—0.37 
—0.34 
—0.45 
—0.38 
—0.24 
—0.16 
—0.03 
+0.03 
+0.1J9 
+C.  17 
+0,19 

// 

+0,06 
—0,10 
—0,02 
+0. 13 
—0,02 
-0,02 
—0,01 
—0.01 
+0.01 
0.00 
+0.02 
—0.03 
—0.09 

// 

+0.03 
—0.04 
—0,01 
+0,03 
—0,09 
—0.06 
+0,03 
+0.03 
+0.08 
+0.04 
0.00 
—0,01 
—0.06 

o 

45 

60 

75 

90 

1(» 

120 

135 

150 

165 

180 

195 

210 

225 

II 

+0,02 
—0,30 
—0.69 
—0.84 
-1.03 
—1.16 
—1.20 
—1.16 
—1.05 
—0.86 
-0.61 
-0,32 
—0.02 

—0.05 
—0.27 
—0.63 
—0,77 
-0.98 
—1.09 
—1,24 
—1.16 
—1.04 
-0,89 
—0,64 
-0,22 
—0,01 

—0.14 
—0,23 
—0.60 
—0.72 
-0.07 
—1.14 
—1.32 
—1.23 
—1.06 
-0,86 
—0.55 
—0.30 
+0.14 

// 

—0.07 
+0.03 
—0.04 
+0.07 
+0.05 
+0.07 
—0.04 
0.00 
+0.01 
—0,03 
—0.03 
+0.10 
+0.01 

-0,16 
+0.07 
—0,01 
+0.12 
+0.04 
+0.02 
—0.12 
—0.07 
—0,01 
0.00 
+0,06 
+0,02 
+0.15 

The  lower  line  of  the  table  is,  it  will  be  seen,  only  a  repetition  of  the  upper  with  the 
sign  changed.     We  always  have 

V        w     .    ,  .  /R+/(R+180O)=0 

by  the  fundamental  hypothesis  of  the  investigation. 

(63)  Values  of  g  z. — Taking  the  differences  of  the  K's,  we  have  eight  distinct  values  of 
8  g.z,  the  sum  of  which  gives  the  value  of  64  gji,  derived  from  the  observation.  The  mean  is 
as  follows: 


0 

+.01 

16 

+0.14 

30 

+0.07 

46 

-0,02 

60 

+0.08 

75 

+0.10 

90 

+0.C8 

105 

+0,06 

120 

+0.02 

136 

-0,04 

150 

+  0.02 

165 

—0.02 

Though  these  values  are  quite  well  marked,  indicating  a  twisting  flexure  coefficient  of 
0".06,  I  am  not  at  all  satisfied  of  their  reality,  and  have  therefore  preferred  to  dispense  with 
their  use,  and  derive  the  telescope  flexure  for  each  end  of  the  axis  directly  from  the  observations. 

(64)  Flexure  of  the  Telescope. — The  preceding  investigation  gives  the  flexure  of  the  circle 
divisions  relatively  to  the  central  nucleus  of  the  circle.  We  next  wish  to  know  the  flexure  of 
the  line  joining  the  micrometer  wire,  and  the  optical  centre  of  the  object  glass  relatively  to 
the  same  nucleus.  During  the  early  part  of  the  year  1866,  I  was  greatly  trooble4  by  finding 
a  constant  difference  of  a  large  fraction  of  a  second  between  the  horizontal  flexnre  determined 
from  the  opposing  and  that  from  the  levelled  collimators.  It  seemed  to  follow  from  this,  that 
if  the  axes  of  the  collimators  were  so*^^  optically  in  the  same  line,  tbe  difference  of  their  level 


H 


mm 


UNITEU   STATES   NAVAL   OB8EBVATORY. 


88 


9  mean  is 


errors  would  not  be  equal  to  their  d  fference  nf  latitude,  m  it  should  be.  On  April  17,  1860. 
this  was  tested  directly,  in  the  following  way:  The  error  both  of  level  and  coUitnation  of  each 
collimator  was  reduced  as  much  as  possible.  The  telescope  was  set  vertically,  the  cube  opened, 
and  collimator  A  turned  till  its  double  wires  were  horizontal.  The  shutters  were  closed,  as 
usual,  in  observing  the  collimators.  Three  observers  were  employed;  one  to  read  the  level 
of  each  collimator,  and  one  to  make  the  images  of  the  horizontal  wires  coincide.  The  latter 
looking  into  collimator  B,  set  the  wires  opposite  in  each  of  the  four  combinations  of  position  of 
the  collimators,  A  90°,  B  180°;  A  90°,  B  0°;  A  270°,  B  0°;  B  180°  and  in  each  combinatitm  a 
set  of  level  readings  of  each  collimator  was  taken.  To  eliminate  any  possible  personal  error 
in  setting,  the  observer  then  went  to  collimator  A,  and  the  operation  was  repeated.    The  result 

was  as  follows: 

Mean  level  of  A,  (North,)        p".87,  (8.  end  high.)  . 

"        "        B,  (SoQth.)        0  .29,        "        "  • 


Dififorence     -    -    • 
Oorr.  for  diff.  of  collars, 
Gorr.  for  diff.  of  latitude, 


+0"  58  8. 
+0  .26 
+0  .25 


Sum 1".09        ,..,:>..-.„■:.,-'  ^     _;■ 

This  sum  ought  to  be  zero,  so  that  there  is  a  seeming  discrepancy  of  1".09.  That  this  is 
due  to  refraction,  I  entertain  no  doubt,  for  the  following  reasons:  (I.)  A  p-iori;  an  increase 
of  temperature  amounting  to  1**  Fahrenheit  in  two  feet,  will  entirely  account  for  it;  and  the 
actual  increase  frona  the  floor  to  the  roof  is  found  to  exceed  this  on  a  sunny  day.  (2.)  A 
few  days  afterward  the  observations  were  partly  repeated  with  the  shutters  open,  and  a  cold 
wind  blowing  through  the  room.  The  discrepancy  was  0".61  in  the  opposite  direction.  The 
images  were  quite  unsteady,  and  the  wind  troublesome. 

(66)  The  flexure  by  the  opposing  collimators  was  determined  by  setting  the  telescope  on 
one  collimator,  and  reading  the  telescope  and  microscope  micrometers.  The  telescope  was  then 
pointed  upward,  and  the  horizontal  wires  of  the  other  collimator  set  on  those  of  the  first.  The 
circle  reading  was  then  determined  for  the  other  collimator,  and  the  telescope  again  pointed  to 
the  zenith.  The  first  collimator  was  then  set  independently  on  the  second,  and  the  two  colli, 
mators  were  thus  alternately  set  and  read  as  often  as  was  deemed  advisable.  The  following 
are  the  separate  results  obtained  on  different  dates: 

1865.  Dec.     16,   /=4-0".15; 


1866.  Mar.    29, 

Apiil  16, 

26, 

May    31, 

Jane    9, 


+0  .83, 


+  1 
+0 
-♦-0 
+0 


.42, 


/'=0".77; 
1  .30; 


.71,  wt.  =1 ; 
.89.  wt.  =2; 
.49,  wt.  =:1. 


After  the  first  determination  the  screws  of  the  object  end  of  the  telescope  tube  were  tight- 
ened. The  two  next  v,ere  made  without  suspecting  that  the  results  might  be  vitiated  by  re- 
fraction, and  therefore  without  attention  to  the  equality  of  temperature  in  the  different  strata 
of  air.  They  are  therafore  rejected.  The  last  three  were  made  with  the  shutters  open,  at 
times  when  the  int'jraal  and  external  temperatures  were  nearly  equal.  That  of  May  31  was 
particularly  satisfactory,  and  depends  on  four  readings  of  one  collimator,  and  three  oi  the  other, 
the  separate  readings  being 


N. 
48".39 

47  .81 

48  .12 
47  .87 


B. 
50".77 

50  .87 

60  .09 


mmnmimmm 


fcVti*a!»^,Uiit'WPrt^'ailK«»«S-  It'^'V^'ftW 


'M  DESCBIPTION    OF   THE  TRANSI1'  CIRCLE   OK  THE 

The  valae  of /,  concluded  from  obsttrvHtions  of  the  opposing  collimatora.  is 

0".76. 

In  the  beginning  of  1867  the  object  glass  was  taken  out  and  cleaned.  Gonceiviug  a 
change  in  the  elasticity  of  its  bearings  possible,  a  careful  determination  of/'  was  made  on 
September  9,  1867.  The  circumstance  taken  advantage  of  to  secure  equality  of  temperature 
was  a  cold  ruin.  Two  thermometers  were  fastened  to  the  stairway  below  the  line  from  the 
object  glass  of  the  telescope  to  each  collimator,  and  two  more  were  suspended  just  under  the 
roof.  The  upper  pair  indicated  a  higher  temperature  of  1°.2  before  tho  observations,  and  2°.2 
afterward.     The  separate  readings  uncorrected  for  circle  flexure  were: 

SonthcoU.  North  coll. 

fi'=90O  B'b270O 
•     14".69  lfi".13 

15.  10  15.  18 
14.  97  16.  26 

16,  43  16.  67 
.,^^   16.61 

The  readings  were  commenced  on  the  south  collimator.  On  looking  into  it  to  set  it  on  the 
north  one,  preparatory  to  its  second  reading,  the  mean  of  wires  were  seen  to  differ  quite  sensibly 
from  coincidence  with  th«i  wire  of  the  other  collimator.  The  first  reading  is  therefore  regarded 
as  doubtful.     The  result  of  these  readings  is 

/'=+0".78. 

During  the  autumn  of  1866  the  levelled  collimators  were  regularly  observed  at  night  with 
the  shutters  open,  so  that  the  mean  result  ought  to  be  free  from  refraction.  The  result,  from 
observations  made  by  Messrs.  Hall  and  Rogers  and  myself,  was: 

Mean  excess  of  reading  for  S.  collimator,         1".86 ; 
,    >    t  Uncorrected  flexure  coefficient  -    - 

,  u^  -  Correction  for  difference  of  latitude 

1,  *i  «rv  difference  of  pivots  - 

circle  of  flexure  •    - 
Resulting  coefficient  .     .    -    .    . 

o  there  is  a  discrepancy  of  more  than  half  a  second  between  the  flexure  coefficients  found  by 
the  two  methods.  The  error  is  probably  in  that  determined  from  the  levelled  collimators,  the 
conical  character  of  their  shoulders  rendering  their  results  uncertain. 

The  discrepancy  is  so  great  that  I  think  it  best  to  try  alio  the  method  of  comparison  of 
direct  and  reflection  observations. 

(66)  Fertiocd  Flexure. — Thus  fiir,  the  coefficient  of  cos  Z  has  been  found  only  by  the  method 
already  set  forth,  namely,  by  comparison  of  the  nadir  reading  obtained  from  observations  of  the 
collimators,  and  that  obtained  directly  by  coinoidenoe  of  the  wires  with  their  images  reflected 
from  mercury .  The  observations  were  so  conducted  as  to  completely  eliminate  every  constant 
error  of  the  collimator  itself,  the  following  b^ing  the  usual  order: 

(1)  Nadir; 

(2)  OoUimator  B  (north); 

(3)  OoltimatorA(sooth);  '    '  ' 

(4)  OoUimator  B  (soadi); 
(6)  OoUimator  A  (north); 
(6)  Nadir. 


0 

.93; 

-0 

.12; 

— 0 

.23; 

-0 

.37; 

-     +C  ,21. 


•Jl 


UNITED  STATES  MAVAL  OBSSRVATORT.  99 

If.  now.  eitlier  collimatoi'  be  nifected  with  any  conntHnt  cnnse  of  error  wlion  on  one  »ido  of 
tlie  inatrament,  lliat  canoe  will  act  in  the  opposite  direction  on  the  circle  reading  when  t'  o  col- 
limator is  carried  to  the  other  side.  By  interchanging  the  collimators  we  therefore  eliminate 
all  constant  errors  pecniiar  to  them. 

The  following  are  the  separate  results  obttined  in  this  way: 


Co 

C-g 

t 

Wt. 

Co 

C\-f 

m. 

1865. 

II 

II 

II 

t/ 

tl 

Dee.  39 

13.  S9 

13.76 

—a  54 

8 

16.35 

15.96 

+0.39 

3 

30 

88.34 

88.44 

-0.10 

a 

33.61 

33.61 

0.00 

3 

1886. 

Jan.  30 

88.34 

88.48 

—0.14 

3 

68.88 

68.78 

--0.04 

3 

Apr.    7 

84.87 

84.96 

—0.09 

3 

18!  43 

14.88 

•■0.04 
-  .0. 11 

3 

16 

19.80 

80.00 

—0.80 

3 

18.38 

.3 

17 

17. « 

17.40 

+0.88 

3 

16.50 

16.66 

—0.16 

3 

.    J8 

1 

11.68 

11.88 

-0.88 

3 

16.44 

16.17 

+0.87 

3 

From  which  results 


g  =:-0".U, 

^=+0".09. 


There  must  always  be  a  possibility  of  the  nadir  determinations  being  affected  with  undis- 
coverable  sources  of  error,  depending  either  upon  the  habits  of  the  observer,  or  the  disturbing 
conditions  to  which  the  instrument  may  be  subjected,  as,  for  example,  the  heat  of  the  observer's 
body.  I  think  it  best,  therefore,  to  depend  for  the  final  value  of  gr  upon  the  comparison  of  ob- 
servations made  in  reversed  positions  of  the  instrument,  the  effect  of  the  cosine  flexure  being 
reversed  with  the  instrument.  For  the  present,  therefore,  the  quantity — 0".14  is  regarded 
simply  as  the  reduction  of  an  observed  nadir  reading  of  circle  A  to  the  mean  of  the  horizontal 
readings. 

'  (67)  In  the  flexure  of  the  telescope  is  included  the  effect  of  gravity  in  changing  the  posi- 
tion of  the  declination  micrometer  slide  relatively  to  the  fixed  plates  of  the  eye-piece.  As  the 
telescope  turns,  the  reading  of  the-  micrometer  for  coincidence  of  the  fixed  and  movable  wires 
is  affected  with  the  inequality 

— 0r.0876  sfa  Z— 0r.0197  cos  Z, 

Z  being  the  zenith  distance  of  the  telescope  counted  in  such  a  direction  that  sin  Z  is  positive 
when  the  micrometer  head  is  above  the  screw,  and  negative  when  below  it. 

The  flexures  alretidy  found  being  corrected  for  this  inequality,  the  value  of  the  sine  coef- 
ficient would  be  quite  small,  while  that  of  the  cosine  coefficient  would  be  increased  to  0".44. 

(68)  In  observing  tSe  sun,  the  aperture  of  the  telescope  is  diminished  to  about  three 
inches  by  means  of  a  cap  weighing  5.3  ounces.  It  is  found,  by  experiment,  that  this  weight 
causes  a  flexure  of — O'MO  fet'n  Z.    A  further  flexure  correction  of 

+0M08inZ 

is  therefore  required  in  reducing  observations  of  the  sun. 


»»»<««f'ffi-?'*!W,'«B!(S*SW*-M«'^«fl'^»«**w^»'»" 


■<^^U<-v4  JJiil!  ■  immisiihW'" 


S6 


L*R8CRIPriON   OF   THi'.  TBAN8IT   CIRCLE   OF  THE 


,  ERRORS  OF  DIVISION. 

(G9)  The  readings  Cor  errors  of  diviaion  of  every  5°  were  made  during  November  and 
December,  18()5,  before  the  cummenceraent  of  astronomical  observations  with  the  instrument. 
The  observers,  beside  mys«!lf,  were  Professors  Hall  and  Eastman,  and  aides  Rogers  and  Thirion. 
Each  observer  rend  two  microscopes.  Any  personal  error  in  reading  will  appear  only  in  the 
distance  of  the  microsfopes. 

A  few  readings  were  tirst  taken  on  the  0°  and  90°  divisions,  with  the  microscopes  90° 
apart,  to  determine  their  angle.  This,  however,  is  of  little  importance,  since  any  error,  in  its 
value,  is  eliminated  in  the  mean  of  four  microscopes,  the  number  always  read  in  astronomical 
observation. 

To  determine  the  error  of  every  45°,  the  microscopes  were  set  45°  apart,  and  both  circles 
were  read  thirteen  times  in  each  of  the  eight  positions.  Assuming  the  error  of  0°  to  he  zero, 
the  following  are  the  resulting  values  of  4e,  or  the  negative  of  four  times  the  correction  for 
error  of  division  for  every  45°: 

*  ,  V'';     Circle  A.  Circle  B. 


0 

0.00 

II 
...       0.00 

46 

-1  19 

—2  87 

90 

-1.12 

—0.80 

130 

-0.67 

-0.69 

To  find  the  errors  of  every  15°,  two  determinations  were  made:  the  first  being  made  with 
the  microscopes  60°  apart,  the  second  with  the  microscopes  75°  apart.  The  circle  was  read 
five  times  in  each  position  in  each  series.  For  circle  A  another  and  more  exact  series  was 
made  with  microscopes  75°  apart. 

The  tirst  series  could  not  give  an  independent  determination  of  the  45°  spaces,  but  the 
latter  did,  and  small  corrections  were  applied  to  them  accordingly;  not,  however,  with  exact 
reference  to  the  forniulsB  for  weights  already  given.     The  following  are  the  results: 


Circle  ▲. 

Circle  B. 

Mic.60. 

76°  (l«t.) 

75°  (8d.) 

Concluded. 

60°. 

75°. 

Concluded. 

o 

II 

It 

tl 

// 

// 

II 

II 

0 

0.00 

0.00 

0.00 

0.00 

0.00 

0.00 

0.00 

15 

—    0.02 

-    0.81 

—    0.18 



0.18 

-    1.73 

—    8.58 

—    8.13 

30 

+    0.14 

+    0.38 

+    0.36 

+ 

0.31 

—    1.07 

—    1.48 

—    1.86 

46 

—    1.19 

—    1.37 

—    1.11 

1.19 

—    8.93 

L-    8.93 

—    8.93 

60 

—    8.89 

—    8.81 

—    8.88 



8.86 

-    3.91 

—    3.88 

—    3.90 

76 

—    1.86 

—    1.79 

—    8.05 



1.79 

-    1.51 

—    0.99 

-    1.86 

90 

—    1.18 

—    1.13 

-    1.18 

.^ 

1.18 

—    0.80 

—    0.80 

—    0.80 

106 

—    0.68 

+    0.03 

—    0.08 

_ 

0.13 

-    1.11 

—    1.07 

—    1.09 

180 

—    1.14 

r-    8.19 

—    1.11 



1.39 

-    1.75 

h-    8.3S 

—    8.03 

136 

—    0.67 

—    0.76 

—    0.68 

_ 

0.07 

-    0.43 

—    0.43 

—    0.43 

180 

-    0.60 

-    1.43 

—    8.88 

,m^ 

1.68 

—    0.94 

—    1.43 

—    1.18 

166 

+    1.16 

+    1.16 

^  0.90 

+ 

1.08 

—    0.13 

—    0.86 

—    0.19 

For  the  errors  of  every  5°  two  series  of  readings  were  made;  one  with  a  distance  of  50°, 
the  other  with  one  of  55°.  Three  readings  wore  made  in  each  po.»ition  of  the  circle  in  each 
series,  except  the  second  series  of  circle  B,  when  only  two  readings  were  made.  The  following 
are  the  separate  results.  The  lust  column  in  each  table  gives  one-fourth  the  negative  of  the 
mean  by  weights  of  the  two  preceding  columns,  and  is  the  correction  to  be  applied  to  the  mean 
of  opposite  microscopes  on  account  of  errors  of  division: 


UNITED  STATES  NAVAL  0B8BRVAT0BT. 


m 


1 

Circle  A. 

Circle  B 

60°. 

66°. 

Concluded 
—  e. 

60". 

65°. 

Conclnded 

o 

// 

// 

•/ 

// 

// 

ti 

0 

0.00 

0.00 

0.00 

0.00 

0.00 

0.00 

5 

+ 

1.44 

+ 

0.89 

—    0.88 

— 

0.86 

—     1.06 

+ 

0.34 

10 

+ 

1.55 

+ 

1.39 

+    0.37 

— 

0.99 

—    0.76 

+ 

0.88 

15 

0.17 

0.18 

+    0.04 
+    0.86 

_ 

3.08 

—    8.13 

0.58 

80 

— 

0.93 

— . 

1.10 

— 

1.96 

—    1.91 

0.48 

86 

— 

1.56 

— 

8.05 

+    0.45 

— 

1.88 

—    8.03 

+ 

0.48 

»0 

+ 

0.34 

+ 

0.3i 

-    0.08 



1.88 

—    1.33 

+ 

0.33 

35 

0.64 

0.96 

+    0.80 

— 

3.77 

—    3.07 

+ 

0.78 

40 

— 

1.41 

_ 

0.83 

+    0.88 

— 

3.19 

-    8.63 

0.74 

45 

_ 

1.19 

- 

1.19 

+    0.30 

— 

3.93 

—    8.93 

0.73 

50 



1.09 



0.08 

+    0.14 

,_ 

3.80 

—    3.33 

■1- 

0.90 

55 

— . 

1.08 

— 

8.89 

4-    0.43 

— 

3.35 

—    3.44 

-\. 

0.85 

60 

_. 

8.88 

— 

8.18 

+    0.55 



3.98 

—    3.84 

+ 

0.97 

66 

_ 

8.80 

_ 

8.38 

+    0.56 

— 

3.47 

—    4.06 

+ 

0.9H 

70 

— 

0.88 



0.36 

+    0.16 

— 

3.83 

—    3.93 

t 

0.88 

78 

_ 

1.79 



1.70 

+    0.44 



1.87 

—    1.31 

0.38 

80 

+ 

1.79 

+ 

8.85 

—    0.51 

_. 

O.I"8 

—    0.96 

+ 

0.13 

85 

0.66 

0.38 

■+■    0.13 
■f    0.88 

+ 

0.84 

—    0.91 

+ 

0.06 

90 

— 

1.18 

_ 

1.18 

0.80 

—    0.80 

+ 

0.30 

95 



8.05 



1.78 

+    0.48 

— 

1.34 

—    1.46 

+ 

0.35 

100 

— 

8.84 

— 

1.36 

+    0.45 

— 

1.81 

—    0.88 

+ 

0.36 

105 

— 

0.88 

— . 

0.13 

+    0.04 

— 

1.06 

—    1.04 

+ 

0.86 

no 

+ 

0.71 

+ 

0.09 

—    0.10 

+ 

0.88 

—    0.89 

0.01 

115 

1.09 

1.04 

+    0.87 

1.33 

-1.30 

0.3:1 

180 

— 

1.51 

— 

1.43 

+    0.36 

' — 

8.07 

—    1.96 

0.51 

185 

_ 

8.86 

— 

0.90 

4-    0.40 
-j-    0.48 



1.10 

—    1.81 

0.34 

130 

— 

1.79 

_ 

8.07 

— 

0.84 

—    0.78 

A. 

0.80 

135 

— 

0.63 

— 

0.67 

+    0.16 

— 

0.43 

—    0.43 

+ 

0.11 

140 

+ 

1.48 

+ 

1.51 

—    0.37 

+ 

0.56 

—    0.03 

0.08 

145 

0.87 

0.08 

+    0.04 

0.16 

+    0.10 

M 

0.08 

150 

— 

1.50 

— . 

1.53 

+     0.38 

— 

1.30 

-    1.81 

^ 

0.38 

155 



0.40 



0.44 

+    0.10 

__ 

1.19 

—    1.41 

+ 

0.33 

(60 

+ 

1.61 

u. 

0.97 

—    0.38 



0.83 

—    0.44 

+ 

0.08 

165 

0.97 

1.09 

—    0.86 



0.18 

—    0.80 

+ 

0.06 

170 

0.89 

0.66 

—    0.19 

— 

0.38 

—    0.11 

0.07 

175 

T" 

0.87 

T" 

0.51 

—    0.17 

"■• 

0.88 

—    0.78 

"T" 

0.18 

We  have  here  two  entirel)-  independent  determinations  of  each  division  error,  except 
those  which  are  multiples  of  16°.  The  mean  difference  between  the  two  values  of  4«  is  0".  52  for 
circle  A,  and  0".4I  for  circle  B.  The  difference  of  accuracy  between  tlie  circles  arines  from 
differences  in  the  eye^sight  of  the  observers.  It  appears  then  that  the  probable  value  of  a 
concluded  e  is  about  0".065  for  circle  A,  and  0".05l  for  circle  B.  The  probable  error  of  the  mean 
reading  of  four  microscopes,  when  these  divisions  are  under  them,  will  therefore  be  about 
0".046  for  circle  A,  and  0".036  for  circle  B,  a  quantity  smaller  than  the  probable  accidental 
error  of  the  isolated  divisions.  Little  advantage  would  therefore  be  gained  by  making  the, 
determination  more  exact. 

(70)  When  the  mean  of  divisions,  90°  apart,  is  taken,  the  progression  of  the  errors  in  the  case 
of  circle  B  are  so  regular  that  a  determination  of  the  intermediate  divisions  was  supposed  to  be 
hardly  necessary.  But,  as  circle  A  was  used  for  all  the  observations  in  1866,  it  was  thought 
desirable  to  determine  at  least  some  intermediate  points  on  that  circle.  Accordingly,  the  micro- 
scopes of  that  circle  were  placed  at  the  distance  43°20',  and  one  complete  series  of  readings  were 
made,  which  gave  the  error  of  every  10°40'.  The  result  ghoived  that  the  errors  of  the  intermediate 
divisions  were  systematicaUy  greater  than  those  of  the  5°  divisions,  the  mean  difference  being  -f-0".  39. 

This  was  supposed  to  indicate  a  cyclical  inequality  in  the  error,  the  period  of  which  was 
5°.  In  order  to  determine  it  accurately,  it  was  necessary  to  determine  the  error  of  every  de- 
gree of  both  circles.  This  was  done  on  September  17-19,  1866.  The  microscopes  of  each 
circle  were  placed  at  the  distance  48°,  and  the  circles  were  both  read  once  in  each  position 
Again  the  result  was  anomalous,  and  the  cyclic  hypothesis  bad  to  be  modi6ed  or  abandoned. 
The  systematic  mean  difference  between  the  5°  divisions  and  the  intermediate  even  degrees 
was  only  0".14  for  circle  A,  and  0".08  for  circle  B. 


w 


f^^ 


38 


DBHCItlPTION    OK   THE   TRANSIT   CIRCLK   OP   THE 


mJi 


A  larit  Htteiiipt  lo  discover  the  f^enernl  liiw  of  the  inequality  without  the  laborioiii)  operation 
of  deterniiiiiiifj;  the  error  of  every  10'  wus  made  in  January,  1867.  The  6°  interval  wa»  di 
v'uUn\  into  six  parts  by  setting  the  microscopes  of  circle  8  44"  10'  apart,  and  this  circlw  was  read 
on<!o  in  each  position.     The  cycle  now  seemed  to  be  reduced  to  30'. 

To  show  the  nature  of  the  law  the  correction  for  the  mean  of  four  microscopes,  as  it  re- 
sulted from  the  above  determination,  is  shown  for  each  circle  in  the  following  tt»ble: 

_  CIRCLE  A. 


Correction  for 

error  of  diviBion  of— 

A 

A+ 

A+ 

A+ 

A+ 

A+ 

A+ 

A 

o 

O         ;    : 

o 

o 

0          ( 

o 

1 

1    40 

8 

3 

3    20 

4 

0 

II 

// 

// 

// 

// 

ft 

// 

0 

--0. 14 

+0.08 

—0.34     —0.10 

-0.05 

-0.84 

+0.07 

5 

-  -0. 13 

+0.10 

—0.20     —0.33 

—0.40 

—0.18 

-0.88 

10 

--0.04 

-0.24 

—0.56     +0.25 

—0.22 

—0.23 

-0.41 

15 

--0.04 

+0.15 

-1-0.02     +0.06 

-0.18 

—0.18 

+0.24 

W 

--0.08 

—0.05 

—0.33     +0.14 

+0.17 

+0.15 

-■0.15 

•25 

+0.35 
-  -0. 14 

-0.17 

-0.64     - 

-0.08 

-0.16 

-0.18 

■-0.08 

:w) 

+0.18 

—0.14     - 

h0.07 

—0.25 

-0.08 

+0.10 
-  -0. 10 

35 

■■0,30 

-  -0. 18 
--0.26 

-0.14     --0.24 

+0.18 
-f.0.35 

—0.08 

40 

--0.38 

-0.08     --O.IB 

+0.02 

+0.22 

45 

--0.23    i-»0,06 

-0.44    ;- 

-0.10 

-0.04 

-0.24 

-0.25 

50 

-fl.  12    i    0. 13 

-0.45     --0.02 

+0.08 

—0.30 

+0.18 

56 

-i  .  23            04 

-0.34     - 

-0.15 

+0.18 
-}-0.20 

—0.18 

-H).30 

GO 

-.•0.4S      r'..58 

-O.07     - 

-0.18 

--0.10 
■■0.04 

-H).08 

65 

U0.33 

+0.15 

—0.12     - 

-0.26 

0.00 

-0.05 

70 

-0.08 

-0.08 

—0.76    ;— 0.18 

-0.16 

—0.78 

-0.16 

75 

i-'.Of 

-0.2(' 

_-fl.48    —0.29 

-0.44 

-0.46 

—0.18 

80 

-fl.3i        ''.S* 

•..E5    —0.40 

-0.43 

—0.48 

—0.29 

85 

—0.02 

--0.  !2 

-0.39     —0.88 

-0.07 

-0.85 

-H).35 

Mean  .     . 

+0.13 

+0.02 

—0.33  ; 

0.00 

-0.08 

—0.19 

+0.08 

M.— <)."13 

0.00 

—0.16 

-0.46     —0.13 

-0.81 

—0.32 

-O.U 

CIRCLE  B. 


A 

. — 

Correction  for  error  of  division  of— 

A+ 

A+ 

A+ 

A+ 

A+ 

A+ 

A+ 

A+ 

A+ 

A 

O         / 

o 

0         / 

0 

O         / 

o 

O        1 

o 

0        / 

0    50 

I    ♦ 

1    40 

8 

8    30 

3 

3    20 

4 

4    10 

0 

II 

It 

// 

// 

// 

It 

// 

II 

// 

II 

0 

-fO.lO 

-0.39 

0.10 

—0.05 

0.18 

-0.09 

0.11 

—0.06 

0.06 

-0.88 

5 

.30 

.04 

—  .01 

.31 

—  .06 

.08 

.85 

—  .06 

.18 

-  .01 

10 

.89 

-  .09 

.14 

.00 

.16 

.86 

.37 

.24 

.04 

-  .05 

15 

.39 

—  .01 

.32 

.34 

.31 

.40 

.10 

.14 

.39 

.14 

20 

.24 

.88 

.88 

.10 

.30 

.31 

.38 

.34 

—  .09 

.01 

25 

.40 

.80 

.84 

.06 

.88 

.86 

.58 

.34 

.16 

.04 

30 

.42 

.16 

.59 

.36 

.33 

.41 

.36 

.54 

.58 

.31 

35 

.53 

.24 

.37 

.46 

.46 

.31 

.38 

.39 

.04 

.16 

40 

.47 

.20 

.47 

.30 

.40 

.61 

.45 

.58 

.43 

.11 

45 

.42 

.08 

.88 

.01 

.03 

.19 

.10 

.80 

.10 

.30 

50 

.41 

.30 

.85 

.16 

.88 

.85 

.81 

.19 

.88 

.16 

55 

.44 

.16 

.39 

—  .04 

.35 

.84 

.15 

.18 

.46 

.89 

60 

.64 

.66 

.82 

.51 

.56 

.64 

.48 

.54 

.30 

.86 

65 

.ei 

.40 

.44 

.48 

.48 

.60 

.58 

.61 

.64 

.89 

70 

.48 

.85 

.53 

.36 

.88 

.39 

.68 

.86 

.37 

.44 

75 

.18 

.80 

.48 

.06 

.88 

.00 

.86 

.11 

.86 

-.04 

80 

.10 

—  .01 

—  .04 

—  .06 

.40 

.80 

.15 

.88 

.88 

—  .04 

85 

0.09 

—0.48 

0.08 

-0.88 

-0.08 

-0.89 

-O.06 

0.01 

-0.16 

-0.88 

// 

tl 

// 

II 

// 

// 

// 

// 

If 

'ii 

MOMI   .      . 

0.36 

0.13 

0.31 

0.16 

0.86 

0.87 

0.38 

0.86 

0.23 

0.09 

M.-0'.'36 

0.00 

—0.83 

—0.05 

-0.80 

~C  10 

-0.00 

—0.08 

—0.10 

—0.13 

-0.8T 

UNITED  STATES   NAVAL   OB8BBTATORY.  ><        flf 

The  8yAtematic  irregnlarity  is  well  marked  in  this  table,  and  HeiMnx  to  follow  the  Rnme  law 
in  the  two  circles,  except  that  it  is  nearly  twice  hh  great  for  A  a»  for  B.  Two  important  quoH> 
tions  now  present  themselves  respecting  the  nature  of  the  law. 

1.  Do  the  intermediate  errors  really  depend  upon  those  of  the  5°  spaces  on  each  side  of 
them  more  than  on  any  other  part  of  the  circle?  If  not,  the  attempt  to  determine  the  errors 
with  precision  might  as  well  be  abandoned.  Innpection  of  the  above  tab^es,  however,  shows 
that  for  circle  B,  at  least,  the  question  is  to  be  answered  in  the  affirmative;  the  corrections  of 
the  intermediate  divisions  increase  and  diminish  with  those  of  the  5<^  ones,  and  to  about  the 
same  extent  with  the  latter. 

2.  Do  the  systematic  errors  of  the  5°  spaces  peculiar  to  them  affect  them  alone,  or  is  the 
law  of  error  continuous?  For  example,  are  the  systematic  errors  of  the  divisions  4°  68'  and 
5°  2' the  same  as  those  of  6°,  or  are  they  the  same  as  those  of  4°  10'  and  5°  60'?  If  the  former,  ' 
the  spaces  on  each  side  of  the  6°  divisions  will  be  equal;  if  the  latter,  they  will  differ  by  half  a 
second.  Twenty  pain,  of  i  itervals  of  circle  B — those  adjacent  to  every  16°  from  0°  to  136°, 
and  from  180°  to  316° — were  measured  and  compared,  and  the  mean  difference  found  to  '  e 
0".07.  The  law  of  periodic  error,  whatever  it  maybe,  is  therefore  continuous.  It  seems 
result,  in  great  part  at  least,  from  two  cycles  in  the  errors  of  division;  the  one  having  a  peric? 
of  6°,  the  other  a  period  of  30'. 

(71)  The  course  which  it  seems  best  to  adopt  is  this:  instead  of  attempting  to  determine 
the  errors  of  division  with  the  last  degree  of  precision,  we  shall  seek  to  eliminate  them  by 
changing  the  position  of  the  circles  from  year  to  year,  so  that  the  poxition  of  any  one  star  will 
depend  on  different  divisions  in  different  years.  If  the  periodic  errors  be  entirely  ne;;lected, 
the  effect  of  their  probable  amount,  at  least  in  the  case  of  circle  B,  will  be  lass  than  C".  I.  and 
the  total  probable  effect  of  the  difference  between  the  actual  and  the  adopted  error  uf  any  iso- 
lated error  of  division  will  not  much  exceed  that  amount.  The  uncertainty  of  the  moan  of 
four  divisions  will,  therefore,  scarcely  exceed  the  probable  error  of  the  declinations  of  funda- 
mental  stars  derived  from  all  the  observations  hitherto  made. 

(72)  To  obtain  a  general  table  of  the  corrections  of  the  divisions,  we  have  first  corrected 
the  determinations  given  in  the  preceding  tables  for  periodic  error,  so  as  to  take  the  mean  of 
the  entire  degree  divisions,  those  which  are  a  multiple  of  6  excepted,  as  the  standard.  This 
has  been  effected  by  applying  the  following  correction;)  to  the  different  vertical  columns: 

Colomn.                   Circle  A.  Circle  B. 

o  t                            It  It 

A                             —0.14  —0.19 

A+0  60                  +  .14 

A4-1                             .00  .00 

A+1  40                +  .32  -f-  .11 

A+2                            .00  .00 

3 +2  30                  .00 

A+3                            .00  .00 

A.+3  20                 +  .16  .00 

A+4                           .00           .  .00 

A+4  10                 +  .18 

The  corrections  are  thus  reduced  to  what  they  would  have  been  had  there  been  no  peri- 
odic  error,  and  arranged  consecutively  in  a  table.  The  mean  difference  between  consecutive 
numbers  was  now  found  to  be  0".160  for  circle  A,  and  0".136  for  circle  B,  indicating  a  prob- 
able error  of  each  individual  determination,  combined  with  the  accidental  error  of  division,  of 
leas  than  0".l. 


; 


; 


I 

1 


40 

Tahit  ^  rerreetumt  to 


OESCRIFTIOM   OP  THE  TEAMSIT  OIROLK   OP  THE 


(ffjimr  mieroieope*  fur  errort  vf  divuiom. 
microwope. 


ArgumefU,  mdimg  ^  hori*<nUal 


Arg. 

Circle  A. 

Circle  B. 

Aiv. 

Circle  A. 

Circle  B. 

o 

II 

(/ 

o 

// 

// 

0 

+0.18 

+0.30 

45 

+0.08 

-0.01 

1 

+  .06 

.83 

46 

.00 

.00 

s 

.00 

.18 

47 

—  .08 

.00 

3 

—  .06 

.18 

46 

—  .04 

.00 

4 

—  .11 

.88 

49 

—  .04 

+  .06 

6 

—  .17 

.87 

50 

—  .04 

.18 

6 

-   .10 

.87 

51 

—  .08 

.18 

7 

—  .08 

.86 

68 

—  .88 

.18 

8 

.00 

.86 

53 

—  .80 

.13 

9 

+  .04 

.87 

54 

—  .16 

.14 

10 

.07 

.89 

55 

—  .18 

.15 

11 

.08 

.89 

56 

—  .12 

.16 

IS 

.10 

.89 

67 

—  .18 

.17 

13 

.13 

.36 

68 

—  .18 

.19 

14 

.80 

•<< 

59 

—  .18 

.80 

15 

.88 

.68 

60 

—  .05 

.88 

16 

.87 

.66 

61 

+  .05 

.86 

17 

.84 

.57 

68 

.06 

.86 

18 

.83 

.57 

63 

.05 

.87 

10 

.80 

.58 

64 

.08 

.85 

80 

.16 

.48 

65 

.00 

.88 

ai 

.17 

.49 

66 

.08 

.28 

82 

.16 

.68 

67 

.09 

.88 

8:» 

+  .10 

.53 

68 

.15 

.82 

84 

-.08 

.50 

69 

.14 

.83 

85 

—  .14 

.46 

70 

+  .08 

.84 

86 

—  .18 

.44 

71 

-.03 

.85 

87 

—  .88 

.48 

78 

—  .18 

.87 

88 

—  .84 

.40 

73 

-  .18 

.88 

89 

—  .80 

.34 

74 

—  .06 

.31 

30 

—  .16 

.87 

75 

+  .04 

.35 

31 

—  .83 

.84 

76 

.04 

.40 

38 

—  .89 

.88 

77 

.02 

.45 

33 

—  .38 

.19 

78 

.00 

.46 

34 

—  .36 

.15 

79 

.01 

.45 

35 

—  .37 

.11 

80 

.18 

.44 

36 

—  .36 

.18 

81 

.16 

.41 

37 

—  .36 

.15 

88 

.17 

.38 

38 

—  .36 

.14 

83 

.18 

.36 

39 

—  .89 

.08 

84 

.19 

.36 

40 

—  .88 

+  ,08 

e& 

.20 

.36 

41 

—  .17 

-.07 

86 

.23 

.40 

48 

—  .18 

—  .12 

87 

.25 

.44 

43 

—  .06 

-  .13 

68 

.25 

.44 

44 

-  .08 

—  .07 

89 

.19 

.37 

45 

+0.03 

-0.01 

90 

+0.18 

+0.30 

The  correctioua  thuB  obtained  wore  now  made  continaous,  and  the  above  table  was  formed 
in  the  following  way.     Represent  the  correction  for  y°  by  (Y).     Then,  for  circle  A  was  taken 

[1^1-  >^  (i)+(l|)+(2)  J.. 

[3H=i<{  (3)+(3t)+(4)  ^ 
&e.t  Ace. 

[Oj=i'{  [88i]+(0)+[l|]  J., 

l«]=H  [3i]+(«)+[6|U. 
[2J]«H  (2)+(3)  ^ 


&. 


dee. 


&c  fcc. 


■''^^^^S^SS^f^-y? 


UMITBD  STATn  HAYAL  OBSBBYATOBT.  m. 

The  concluded  corrections  were  then  interpolated  between  [0],  [[2^]],  [6],  [[7|]],  Ao. 
For  circle  B  was  taken 

[i*]«H  (t)+(i)+(ii)+(8)  y, 

[Sil-H  (3)+(34)+(4)+(4j)  }, 
•  tcct  cbc. 

(0]-t^[8^)+(0)+fli]}.. 

[7i]^u*m]Hn)+m]>. 

oCC.t  «cc> 

The  condaded  corrections  were  then  interpolated  between  [0],  [2)],  [5],  [11^],  Ac. 
In  the  table  the  argument  is  changed  45°,  so  as  to  correspond  to  the  reading  of  the  finding 
microscope. 

ERRORS  OF  CERTAIN  ISOLATED  DIVISIONS. 

(73)  During  the  year  1866  the  circle  was  so  set  that  when  the  telescope  pointed  toward 
the  nadir,  the  reading  of  the  finding  microscope  was  359°  56' .  It  therefore  becomes  necessary 
to  determine  the  error  of  the  particular  divisions  then  under  the  microscopes,  relatively  to 
the  others.  For  this  purpose  microscope  YII  was  furnished  by  the  machinist  of  the  Observ* 
atory  with  two  extra  pair  of  spider  lines  at  a  distance  of,  as  nearly  as  possible,  2^  on  each  side  of 
the  central  pair.  Each  division,  from  44°  42'  to  45°  8',  was  then  brought  in  succession  under 
the  middle  pair  of  wires,  and  at  each  setting  the  three  pairs  were  placed  in  succession  over 
their  corresponding  divisions.  Thus,  two  measures  of  each  space  were  obtained.  These 
measures,  being  treated  in  the  way  already  set  forth,  gave  the  following  corrections  for  each 
division  relatively  to  the  mean  of  the  fourteen  divisions  from  44°  42'  to  45°  8',  134°  42'  to 
136°  8',  Ac: 


DlY. 

Cor. 

Div. 

Cor. 

DIv. 

Cor. 

Dlv. 

Cor. 

Mora. 

O         ' 

(/ 

0          / 

// 

o        / 

II 

O           ' 

it 

II 

44    48 

+0.86 

134    48 

+0.87 

384    48 

-0.01 

314    48 

+0.18 

+0.16 

44 

+  .19 

44 

+  .07 

44 

—  .09 

44 

—  .09 

+('.08 

46 

-.09 

46 

-.31 

46 

—  .83 

46 

—  .11 

—0.18 

48 

—  .06 

48 

-  .01 

48 

+  .03 

48 

+  .01 

0.00 

60 

—  .06 

60 

+  .03 

60 

—  .07 

60 

-.83 

-0.08 

68 

+  -*ih 

68 

—  .04 

68 

+  .10 

68 

+  .« 

+0.08 

64 

—  .18 

64 

—  .09 

54 

.00 

64 

-.86 

—0.18 

66 

-  .06 

66 

—  .13 

—  .81 
+  .81 

56 

--  .09 

56 

—  .08 

—0.04 

68 

+  .36 

68 

68 

--  .40 

68 

+  .09 

+0.16 

46      0 

—  .03 

136      0 

885      0 

-•  .04 

315      0 

+  .10 

+U.08 

8 

—  .08 

» 

+  .43 

8 

—  .01 

8 

-.08 

--O.08 

4 

—  .86 

4 

—  .03 

4 

—  .11 

4 

—  .14 

—0.13 

6 

—  .14 

6 

—  .19 

6 

+  .04 

6 

+  .a 

—0.08 

8 

+  .19 

8 

—  .01 

a 

—  .80 

H 

+0.16 

+0.04 

TESTS  FOR  OTHER  POSSIBLE  ERRORS. 


J  - 


(74)  The  errors  of  an  instrument  may  be  divided  into  two  clatwes;  those  which  we  expect 
to  find,  determine,  and  allow  for  in  the  reduction  of  observations,  and  those  we  expect  the 
6 


42 


DBSosipnoif  or  ths  tbariit  oisolb  op  ths 


1(* 


,.  i 


111 


I*  § 


artist  to  avoid  entirely,  or  at  least  render  insenaible.  The  olaaaifioation  is  somewhat  arbitrary, 
depending,  as  it  does,  upon  the  degree  of  precision  sought  by  the  astronomer,  and  the  degree 
of  excellence  attained  by  the  artist ;  yet  the  custom  of  astronomers  has  rendered  it  quite 
definite.  The  errors  we  have  investigated  are  generally  recognised  as  of  the  first  class;  we 
shall  now  consider  those  of  the  second. 

(76)  IrregularUy  of  Pivot*. — No  apparatus  fur  determining  directly  the  influence  of  possible 
irregularity  of  pivots  upon  the  axis  of  rotation  was  furnished  with  the  instrument,  but  the 
artists  did  furnish  an  extremely  delicate  instrument  for  determining  any  difference  nf  diameters 
of  the  same  pivot.  It  consists  of  a  pair  of  calipers,  which  are  screwed  upon  one  of  the  Y 
bearers,  and  grasp  the  horissontal  diameter  of  the  pivot.  The  telescope  being  turned,  any 
change  in  the  distance  of  the  calipers  amounting  to  the  two  hundred  thousandth  of  an  inch 
will  be  rendered  sensible  by  a  pair  of  multiplying  levers,  the  end  of  the  last  of  which  moves 
over  a  divided  scale.  The  telescope  being  turned  through  an  entire  revolution  with  the  cali> 
pers  on  one  pivot,  no  difference  of  diameters  so  great  as  this  was  detected.  Only  one  pivot 
was  thus  tested. 

As  an  additional  test,  the  hanging  level  was  placed  upon  the  pivots,  and  read  at  every  20° 
of  zenith  distance  of  telescope,  from  20°  to  160°;  the  telescope  being  moved  by  one  of  the 
west  handles.  It  was  then  returned  by  the  same  handle,  and  the  readings  repeated.  The  effect 
of  the  pressure  of  the  handle  in  changing  the  level  of  the  pivot  was  quite  sensible,  amounting 
to  0".  25 ;  but  this  effect  was  reversed  by  the  backward  motion,  and  the  extreme  range  of  the 
mean  level  reading  for  different  positions  of  the  telescope  was  0".05.  It  was  conc'uded  that 
the  form  of  the  pivots  might  be  regarded  as  perfect. 

(76)  Another  possible  source  of  irregularities  in  the  motion  of  the  optical  axis  of  the  tele- 
scope at  first  caused  me  considerable  solicitude.  It  has  been  seen  in  the  description  that  the 
fulcrum  of  the  levers  of  the  great  counterpoises  are  not,  as  I  conceive  they  should  be  in  so  large 
an  instrument,  knife  edges,  but  pivots.  Owing  to  the  unavoidable  friction  of  these  pivots,  and 
also  to  the  friction  of  the  end  springs,  the  instrument,  when  balanced  by  the  counterpoises, 
will  allow  changes  of  weight  of  perhaps  eight  or  ten  pounds  without  causing  motion  of  the 
lever.  Consequently,  the  division  of  the  weight  between  the  friction  rollers  and  the  pivots 
will  be  uncertain  to  this  amount.  If,  now,  there  bo  uny  irregularity  in  the  grooves  of  the  axis 
by  which  the  friction  rollers  act  on  the  instrument,  this  division  may  vary  in  different  positions 
of  the  instrument,  the  friction  roller  acting  more  powerfully  on  points  more  distant  from  the 
centre  of  rotation.  And  such  a  change  of  pressure  will  produce  a  vertical  flexure  of  the  axis, 
which  will  change  the  direction  of  the  optical  axis  of  the  telescope.  To  avoid  any  possible 
error  from  this  source,  small  pieces  of  rubber  cloth  were  inserted  in  the  sustaining  sockets  on 
the  levers,  the  elasticity  of  which  would  take  up  any  minute  irregularities  of  the  kind  referred 
to,  and  make  the  pressure  nearly  constant. 

To  test  the  effectiveness  of  this  contrivance,  a  piece  of  thin  paper,  probably  7^  of  an 
inch  thick,  was  drawn  under  the  friction  rollers,  and  the  effect  upon  the  level  of  the  axis  and 
the  verticality  of  the  teloscope  was  noted.  The  former  waa  not  changed  at  all.  The  latter, 
which  was  determined  by  comparing  the  position  of  the  vertical  middle  wire,  and  its  image 
reflected  from  mercury,  did  not  admit  of  exact  measurement,  as  the  image  was  nearly  hidden 
by  the  wire.  Certainly,  however,  there  was  no  change  as  great  as  0".S.  The  paper  being 
many  times  as  thick  as  any  probable  irregularity  in  turning  the  axis,  there  is  little  danger  of 
error  from  the  source  in  question. 

(77)  Part  of  the  same  general  investigation  was  the  determination  of  the  effect  en'the  level 
of  the  axis  when  the  action  of  the  counterpoise  was  changed  from  its  maximum  to  its  minimum 
amount.  One  pivot  being  raised  from  its  Y,  by  pressing  on  the  counterpoise,  was  gently  let 
down  ngain,  and  the  level  carefully  noted.     It  was  then  pressed  downward  by  pressing  the 


UMITKD  8TATM  NATAL  OBSmVATOST 


48 


oonnlerpoiM  upward,  and  the  level  again  noted.  The  changes  of  reading  varied  from  0".3  to 
1".0.  They  are,  I  conceive,  almnat  entirely  due  to  flexure  of  the  Y'a  under  the  weightH  of  the 
"ivots. 

(78)  Ooincidenre  of  the  Divided  Facet  <^  the  Cirdet  with  Ptama  perpendtcvlar  to  the  Axis  of 
Botation — There  is  no  error  in  tbia  respect  which  affects  the  definition  of  the  divisionH  in  the 
Belds  of  the  microscope,  and  I  have  made  such  measures  as  to  satisfy  myself  that  no  appreciable 
error  arises  from  the  product  tan  A  it,  p.  11-12. 

(79)  Oenercd  Bemark. — Beside  the  above  systematic  examinations,  the  instrument  is  from 
time  to  time  in  an  irregular  way  examined  for  every  cause  which  I  can  think  of,  as  liable  to 
vitiate  the  results  of  observations.     Nothing  serious  has  yet  been  detected. 


#.1 


*«* 


PART   IV. 


REMARKS  ON  THB  PBRFORMAi^CB  AND  USB  OF  THE  TRANSIT  OIROI.E. 

(80)  The  general  design  of  the  inttrament  ia  entirely  that  of  the  makem.  Specific  direc- 
tions were  sent  them  only  on  a  few  minor  points,  saoh  as  the  arrangement  of  the  micrometers, 
the  self- registering  micrometer  head,  and  the  wires  of  the  retioale.  It  was  the  opinion  of 
Captain  Oilliss,  that,  considering  the  repataion  and  expent.aoe  of  the  artists,  he  would  be 
more  likely  to  secure  a  good  instrument  by  allowing  tiiem  U  carry  out  their  own  vIbwh,  and 
holding  them  responsible  for  the  performance  of  the  instrument   &han  by  designing  it  himself. 

As  a  general  remark,  it  may  be  said  that  the  mechanical  execution  of  every  part  of  the 
instrument  is  of  the  first  order  of  excellence.  I  cannot  speak  with  certainty  of  the  object  glass, 
as  it  has  not  been  severely  tested.  Oertainly,  however,  it  has  no  defect  which  interferes  with 
the  performance  of  the  instrument.  After  being  transported  by  land  and  water  a  fourth  of  the 
way  round  the  globe,  all  tli  delicate  and  complicated  parts  of  the  instrument  were  put  together 
without  impediment  or  dumy,  and  immediately  went  into  successful  operation. 

As  a  knowledge  of  the  defects  in  design  and  performance,  which  we  have  thus  far  suc- 
ceeded in  discovering,  may  be  valuable  to  astronomers,  I  shall  set  them  forth. 

The  only  defects  of  design  which  can  yet  be  pronounced  upon  with  certainty  have  already 
been  alluded  It).    They  are : 

1.  Making  the  zenith  distance  micrometer  carry  the  slides  of  the  ocular,  thus  causing  the 
screw  to  carry  too  much  weight  when  the  head  points  downwards. 

2.  The  form  of  the  supporting  fulcmms  of  the  counterpoise  levers. 

3.  The  instability  of  the  collimators  and  their  levels,  owing  to  the  small  distance  (22  inches) 
between  the  supporting  shoulders.  The  only  inconvenience  which  results  from  this  construc- 
tion is  the  increased  labor  of  levelling  the  collimator. 

(81)  StabUUy  qfthe  Instrument. — ^Invariableness  of  instrumental  constants  is  generally  con. 
sidered  one  of  the  most  desirable  qualities  in  a  meridian  instrument.  A  deficiency  in  this 
respect,  however,  need  not  vitiate  the  results  of  observations,  if  only  the  astronomer  can  deter* 
mine  and  apply  the  constants  with  a  frequency  proportioned  to  the  instability  of  his  instrument. 

The  most  precise  way  to  measure  and  indicate  the  variableness  or  uncertainty  of  the  instru- 
mental constants  is  to  take  the  mean  difference  between  consecutive  determinations  of  the  con- 
stants. This  I  have  done  for  the  latter  part  of  the  year  1866,  and  the  results  are  given  in  the 
following  table.  During  the  summer  of  1867  the  stability  of  the  zenith  point  has  decidedly 
improved,  the  mean  difference  being  reduced  to  0".60. 

Collimation,  October,  1866,  to  July,  1867      -    -    •    -interval  1  week  ■     •     -    -  (K'.23 


Level,  Jnly  to  November,  1866 interval  1  to  4  days-    - 

Level  on  consecative  days interval  1  day     •    •    • 

Mean  difference  of  consecative  transit  of  Polaris  -    -    •  interval  1  day    •    -    - 

Resoltiog  mean  change  of  axfmath interval  1  day    •    -    • 

Zenith  point interval  3  to  12  hours  - 

Inclination  of  £.  pier    ...........  interval  1  day    .    .    - 


0"51 
0".89 
3t.  2 
1".  6 
0".  1 
0".65 


i 


|B|HilS'M'^WliiiW'''MWBtt>^^ 


46 


DK8CR1PTION   OP  THE   TRANSIT   CIRCLE   OP   THE 


*  .> 


If  e  be  tlio  meun  error  of  the  detormination  itself,  we  raay  expect  a  mean  difference  of 
■\/2e  owing  (o  tiiat  error  alone,  supposing  the  instrument  to  remain  invariable.  The  stability 
of  the  line  of  collimiition  may  therefore  be  regarded  as  perfect,  and  that  of  the  level  error 
practically  so,  if  determined  for  each  day  of  observation. 

It  is  far  otherwise  with  the  zenith  point  and  the  azimuth.  Not  only  are  they  variable  to 
an  annoying  degree,  but  the  causes  of  the  variations  are  not  definitely  determined.  Home  light 
may,  however,  be  thrown  upon  them. 

(82)  Zenith  Point. — Previous  to  any  trial  of  the  instrument,  its  most  objectionablo  feature 
seemed  to  bo  the  mode  of  mounting  the  microscopes,  and  many  astronomers  would  have  pre- 
dicted instability  from  this  cause.  But  the  relative  positions  of  the  microscopes  have  proved 
unexpectedly  steady.  The  following  table  shows  the  amount  by  which  the  line  through  the 
zero  of  V  and  VII  was  in  excess  of  90°  from  that  through  VI  and  VIII,  at  various  dates  between 
June  29  and  September  17,  1866,  the  longest  interval  as  yet  in  which  the  microscopes  have 
been  subjected  to  no  disturbance.  They  are  formed  by  subtracting  the  mean  reading  of  V  and 
VII  for  the  two  collimators,  from  that  of  VI  and  VIII,  and  are  therefore  the  difference  between 
the  nadir  points  of  the  circle  as  given  by  the  two  pairs.  The  dates  are  taken  at  random,  except 
with  reference  to  the  observer: 

Date. 


A. 


1866. 


•M'^ 


y&'ik'^'ii-- 


;'.&}^y:. 


June  29, 

// 
+  0.05; 

29  9. 

+  0.02; 

July     2, 

-0.12 ; 

—0.08 ; 

9, 

-0.05 : 

12. 

-0.32 ; 

26, 

-0.10; 

30. 

+  0.30; 

Aug.    6, 

+  0.32; 

15, 

—0.20 ; 

20, 

—0  28; 

29, 

+  0.15; 

Sept.    3. 

-0.16; 

10, 

+0.12; 

14. 

-0.16. 

I  am  persuaded  that  this  degree  of  steadiness  has  never  been  exceeded,  so  that  if  the  cen- 
tral  core  has  been  sot  in  the  pier  in  such  a  way  as  m  secure  immobility,  the  positions  of  the 
microscopes  relative  to  the  pier  will  be  as  invariable  in  this  mounting  as  in  any  other. 

Passing  from  the  microscopes  to  the  circle — the  nicety  of  fit  and  firmness  of  connection  of 
every  part,  from  the  divisions  of  the  circle  to  the  ends  of  the  tube  of  the  telescope,  is  beyond 
reasonable  doubt. 

The  constancy  of  position  of  the  optical  axis  of  the  tube  is  rendered  highly  probable  by  the 
steadiness  of  the  error  of  coiiimation.  Moreover,  the  object  end  of  the  telescope:  has  been  sub- 
jected  to  shocks  several  times  greater  than  it  ever  receives  in  ordinary  use,  without  any  effect 
upon  the  nadir  point. 

The  constancy  of  the  reading  of  the  zenith-distance  micrometer  head  for  a  given  position 
of  the  wires  is  all  that  could  be  desired. 

(83)  Supposing,  from  these  considerations,  that  the  changes  observed  must  be  due  to  move- 
ments of  the  pier  itself,  a  horisontal  cylinder  was  fastened  to  it  in  July,  admitting  of  being 
levelled  by  one  of  the  collimator  levels  and  the  changes  in  the  inclination  of  the  pier  thus 
determined.  But  the  changes  of  nadir  point  were  still  only  partially  accounted  for,  and  the 
correct  nadir  reading  sometimes  exhibits  a  progressive  change,  continuing  through  a  period  of 
several  days. 


T7NITBD   STATES   NAVAL   OBSERVATORy. 


47 


(84)  Apparently,  the  only  untested  link  in  the  chain  ia  the  stability  of  the  setting  of  the 
microscope  holder  (D,  plate  lY,  D-P,  plate  YI,  Fig.  2)  into  the  pier.  To  insure  the  solidity 
of  this  setting,  a  hole  was  cut  from  the  top  of  the  pier  to  the  perforation  which  received  the 
core  of  the  holder,  and  the  plaster  poured  in  until  the  hol«)  was  full,  when  it  oozed  out  on  all 
aides  of  the  core.  The  setting  is,  therefore,  as  solid  as  it  can  be  with  plaster.  It  will,  indeed, 
yield,  and  allow  the  microscopes  to  turn  by  a  strong  pressure  of  the  hand ;  but  under  pressures 
several  times  as  great  as  they  are  ever  subject  to  in  observing,  the  microscopes  are  not  dis- 
turbed at  all.  Still,  consi'jering  the  known  hygrometric  qualities  of  plaster;  considering,  also, 
that  the  relative  readings  of  the  microscopes  on  the  two  piers  are  subject  to  changes  of  the 
same  general  character  and  magnitude  with  the  zenith  point,  I  decidedly  think  that  ''^e  greater 
part  of  the  instability  of  the  zenith  point  is  due  to  the  want  of  firmness  of  the  plaster  setting. 

(85)  The  Azimuthal  Error. — 0^  the  cause  of  the  variation  of  azimuth  I.  entertain  little 
doubt.  The  extreme  breadth  of  the  masonry  on  which  the  piers  are  supported  is  only  four 
and  a  half  feet  from  north  to  south.  With  so  narrow  a  base  injurious  changes  of  inclination  of 
the  piers,  from  motion  of  the  ground  and  consequent  tipping  of  the  masonry,  seem  to  me  un- 
avoidable. And  that  such  clfanges  do  take  place  is  shown  conclusively  by  the  levelling  appa* 
ratus  attached  to  the  piers.  If  every  part  of  the  masonry  tipped  equally,  the  nadir  point 
alone,  and  not  the  azimuth,  would  be  affected.  But  since  the  masonry  is  not  perfectly  rigid, 
this  condition  would  be  fulfilled  only  by  the  ground  giving  way  equally  at  each  end  of  the 
pier,  which  we  have  no  reason  to  suppose  the  case.  The  piers  tipping  unequally,  we  may  look 
for  changes  of  azimuth  us  well  as  of  nadir  point.  The  height  of  the  axis  above  the  centre  oK 
the  pier  being  three  times  the  distance  of  pivots,  the  change  of  azimuth  from  the  cause  in 
question  will  be  three  times  the  change  of  relative  inclination  of  the  piers. 

(86)  In  the  spring  of  1867  a  levelling  cylinder  was  attached  to  the  west  pier  also,  and  the 
difference  of  tipping  of  the  piers  compared  with  the  changes  of  azimuth.  The  latter  were  not 
accounted  fur,  a  fact  which  may  be  attributable  to  the  imperfections  of  the  apparatus  itself. 

(87)  Dependence  of  the  CoUimation  Error  on  Temperature. — Toward  the  end  of  the  year  1866 
the  amount  of  this  error  was  found  to  be  dependent  on  the  temperature,  varying  0".05  for  ewery 
degree  of  Fahrenheit.  The  cause  was  discovered  when  the  object  glass  was  taken  out  at  the 
end  of  the  year.  It  was  then  found  that  the  glass  was  held  in  its  cell  by  the  pressure  of  three 
chucks,  120°  apart,  two  of  them  being  fixed,  Aud  the  third  pressed  in  by  a  strong  spring.  The 
direction  of  action  of  the  spring  was  horizontal.  Hence,  owing  to  the  different  expansibilities 
of  the  brass  and  glass,  the  centre  of  the  latter  would  take  different  positions  relative  to  the 
centre  of  the  former  at  different  temperatures.  The  calculated  change  of  collimation  on  the 
hypothesis  of  perfect  rigidity  of  both  object  glass  and  cell,  is  0".07.  The  difference  between 
this  and  the  observed  change  is  probably  due  to  the  fact  that  the  spring  is  not  perfectly  flex- 
ible, nor  the  glass  and  brass  perfectly  rigid. 

(88)  It  is  probable  that  such  changes  will  ultimately  be  made  in  the  mounting  of  the  object 
glass,  the  microscope  holders,  and  the  great  piers  as  may  seem  sufficient  and  necessary  to 
secure  greater  in>:iiobility  of  the  collimation,  azimuth,  and  zeiiitii  point,  the  instability  of  the 
two  latter  arising,  as  has  been  seen  from  defects  of  mounting  rather  than  of  construction. 


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ALPHABETICAL  INDEX. 


(THE  NU1IBEB8  HEFEB  TO  TH|^  PABAGBAPH&) 


Azb,  dataila  of 

twkt  of,  daring  roTolaUon 

teste  of  ite  motion 

lorel  of,  afftcted  hj  oonntorpoiM. . . 

end  tprinff  of 5. 

AiimnUi,  amonnt  of  ite  ehuigM.. 


33 
«3 
75,76 
77 
18 
80 
85 
4.21 
SI 


Cireles,  diMnetor  anddivisfcwia 

owHagof 

Law  faatenedtoub ao 

perpendienlvitjr  of,  to  azie • 78 

lawf  of  floxnre  of. 61 

table  of  flasnin.. .4 02 

Cirale  dirifiona.    (flte  DiTiakna.) 

Clamp,  deaoriptionof 89 

CSolUmation  error,  ohanfesof. 81 

depead  on  tamporatare , • 87 

OolUmatoia,  deseriptionof 37 

Y'«  of. 38 

maj  be  aet  on  each  otber ^ 5,!i4 

difforenoea  and  form  of  eoUara  of 63 

diacrepaneiea  o^  due  to  refica^ion 64 

reoaaaaafor  pladng 1 

Connterpdaea,  action  of. „ 13 

aflact  level 77 

posaible  bad  ellitet  of,  bowteatad 76 

Cube,  oantial,  of  axia S4 

Deaignof  tba inatmmant,  Uatory  and defcota of „ 80 

Diviaiona  of  eireia,  number  and  thtckneas 91 

formula  for  wrofa '60,51 

errora  of;  iaoiated 51-73 

table  for  evei7  6C< 69 

10 78 

cjoUeal,  inequality  of. 70 

bowteatad 71 

Bnma,  general  pncaotion  againat 79 

inatnuHintal,  table  of  inrtabUity  of 81 

Eya-fieoe,  dewsription  «rf 86-88 

Flwnre .  39 

fhndamantal  hypotberia  in  Inireatigattng 40 

geaatal  tbaomnof 4i 

requititH  for  determining 48-45 

of  drda,  apedal  invaatigation  of 60 

ebawrved  lawaof 61 

tabloof 68 

of  talaeeope,  general  metbod ^ 48 

preeautiona  in  daterminiog 40,64 

produoad  b7  ann  oqt 08 

vertteal,  or  ooaine 48,66 


"M 


3 


i 


■W^ 


50 


ALPHABETICAL  INDEX. 


^f  3 


Flazureof  dedinAtion  micrometer  snppoiti., 07 

twisting,  of  (uii * 63 

Floor,  level  of , 9,11 

IlluminatioD,  lamps  for 34 

of  the  field 38 

ofthewirea  on  dark  field 36 

of  mieroeoopes » • 10,34 

Lerela,  tpirit,  valne  of  divisioiu ..i 6S 

Level  error,  cbuigei  of 81 

Micrometer,  general  deacription  of  ■erawi 39 

declination,  how  moved 89 

Bogeri'B  Mlf-registering  head df* 

periodic  ineqoalitiee  of..... « 66 

-  value  of  ravoiation  of 67 

irregularity  of  motion  of 66 

right  aacension,  deacription  of 96 

revolution,  &o.,  of 69 

wireaof.    (SMWirea.) 

of  nticroacopea.    (8m  MicroscqMa.) 

Mioroacopea,  at^a for  obaerving ....« <...... 8 

mounting  of » • 14 

a^jnatment  of  focua * •••  16 

illnmiMtiou  of 16,34 

dimenalona  and  power 17 

relative  ateadineas  of , ...  88 

probable  uuateadineaa  of  holder 84 

micrometera  of • 64 

deacription  of  Uwir  pwiodic  iaeqoalitiea 66 

of  their  irregnlaritiea 17 

Nadir  point,  platform  and  aeata  for  obaarving ..«. 6,7 

Object  glaaa,  aperture  of •. 3 

mode  of  mounting 87 

Piera,  form,  material,  and  dimenaioua.  ^ 8 

aupporting  maaonry  of. 10 

changea  of  their  inclination 81,83,86 

Pivota,  teat  of  their  form • 78 

dimenaiona  of. --.. 19 

Powera,  magnifying,  of  oculars 31 

B^lroad,  for  reversing  carriage 11 

Ejection  observations,  faoilitiea  fi>r  making 6 

Befraotion,  atmospheric,  inimical  to  flexure  inveatigatiou 49,64 

Room,  dimensions  of. •- J 

details  of - » 

Stability  of  instmment,  tables  of. , 81 

Telescope,  dimenaiona  of ^ - 3 

Wirer,  of  declination  micrometer • 80,33 

of  right  asceaaion  micrometer 87,38 

of  microscope  micrometers >•. '•  17 

fixed,  of  diaphragm,  how  carried • 88 

ufiangemant uid  notation • 38 

how  used  in  observation 39 

Zenith  point,  changes  of 81,88,84 


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